 7.7.4.1: xx 7and 1x 7 have like denominators. x 5x 7and 4xx 7have ______ den...
 7.7.6.1: Equations that contain one or more rational expressions, such as xx...
 7.7.8.1: A ____ is the quotient of two numbers or the quotient of two quanti...
 7.7.7.1: In this section, problems that involve: moving vehicles are called ...
 7.1: Find the values of for which the rational expression x 1x2 16 is un...
 7.7.3.1: The rational expressions 7 6n and n 1 have the common ______ 6n.
 7.7.5.1: The expression 23 1xx 34is called a _____ rational expression or a ...
 7.7.2.1: The ______ of x2 6x 110x6 is 10xx2 6x 1x.
 7.7.1.1: A quotient of two polynomials, such as x2 xx2 3xC, is called a ____...
 7.7.4.2: The polynomials x 3 and 3 x are _____.
 7.7.6.2: To ______ a rational equation we find all the values of the variabl...
 7.7.8.2: A _____ is a mathematical statement that two ratios or two rates ar...
 7.7.7.2: In the formula W = rt, the variable W stands for the _____ complete...
 7.2: Evaluate x2 1x 5 for x 2 x
 7.7.3.2: The ______ common denominator of x 8 and 6 5x is x(x 6).
 7.7.5.2: In a complex fraction, the numerator is above the ______ fraction b...
 7.7.2.2: A ______ conversion factor is a fraction that is equal to 1, such a...
 7.7.1.2: To simplify a rational expression, we remove common _______ of the ...
 7.7.4.3: Write each denominator in factored form. a. x 120x2b. 3x2 4x2 4x 12
 7.7.6.3: To ______ a rational equation of fractions, multiply both sides by ...
 7.7.8.3: In 503 x9, the terms 50 and 9 are called the _____ and the terms 3 ...
 7.7.7.3: Choose the equation that can be used to solve the following problem...
 7.3: Simplify each rational expression, if possible. Assume that no deno...
 7.7.3.3: To _____ a rational expression, we multiply it by a form of 1. For ...
 7.7.5.3: Method 1: To simplify a complex fraction, write its numerator and d...
 7.7.2.3: a. To multiply rational expressions, multiply their ______ and mult...
 7.7.1.3: Because of the division by 0, the expression 80 is _______.
 7.7.4.4: The factorizations of the denominators of two rational expressions ...
 7.7.6.4: When solving a rational equation, if we obtain a number that does n...
 7.7.8.4: The _____ products for the proportion 52 6x are 5x and 12.
 7.7.7.4: Fill in the blank: If a job can be completed in hours, then the rat...
 7.4: Simplify each rational expression, if possible. Assume that no deno...
 7.7.3.4: 16n 8n3 and 2 n2 are _____ expressions. They have the samevalue for...
 7.7.5.4: Method 2: To simplify a complex fraction, find the LCD of _____ the...
 7.7.2.4: Simplify each expression. (x 7) 2 55(x 1)(x 7)(x 9)
 7.7.1.4: The binomials x 15 and 15 x are called ______ , because their terms...
 7.7.4.5: What is the LCD for x 1x 6 and 1x 3?
 7.7.6.5: Is 5 a solution of the given rational equation? a. 1x 1 1 3x 1b. xx...
 7.7.8.5: Examples of _____ prices are $1.65 per gallon, per day, and $50 per...
 7.7.7.5: a. It takes a night security officer 45 minutes to check each of th...
 7.5: Simplify each rational expression, if possible. Assume that no deno...
 7.7.3.5: To add or subtract rational expressions that have the same denomina...
 7.7.5.5: Consider: x 34112 x6a. What is the numerator of the complex fractio...
 7.7.2.5: Simplify each expression. y y y(15 y)y(y 15)(y 1)(x
 7.7.1.5: When we simplify , the result is . These equivalent expressions hav...
 7.7.6.6: A student was asked to solve a rational equation. The first step of...
 7.7.4.6: The LCD for 19n2 and 37 315n3 is 3 3 5 n n n 45n3. If we want to ad...
 7.7.8.6: Two triangles with the same shape, but not necessarily the same siz...
 7.7.7.6: Hospitals. An experienced employee can sterilize an operating room ...
 7.6: Simplify each rational expression, if possible. Assume that no deno...
 7.7.3.6: When adding or subtracting rational expressions, always write the r...
 7.7.5.6: Consider the complex fraction: 1y 1356 1ya. What is the LCD of all ...
 7.7.2.6: a. Write 3x 5 in fractional form. b. What is the reciprocal of 18x?
 7.7.1.6: Determine whether each pair of polynomials are opposites. Write yes...
 7.7.6.7: Consider the rational equation xx 3 1x 2x 3a. What values of make a...
 7.7.4.7: Fill in the blanks. To build xx 2so that it has a denominator of 5(...
 7.7.8.7: Fill in the blanks: In a proportion, the product of the extremes is...
 7.7.7.7: a. Solve for d = rt for t. b. Solve I = Prt for P.
 7.7: Simplify each rational expression, if possible. Assume that no deno...
 7.7.3.7: The sum of two rational expressions is 4x 45(x 1). Factor the numer...
 7.7.5.7: Fill in the blanks. 12y24y3means 12y2 4y3
 7.7.2.7: Find the product of the rational expression and its reciprocal. 3x ...
 7.7.1.7: Simplify each expression, if possible. a. x 8 x 8 b. x 8 8 x c. x 8...
 7.7.6.8: A student solved a rational equation and found 8 to be a possible s...
 7.7.8.8: Is 45 a solution of 53 75x?
 7.7.4.8: Fill in the blanks. To build 8x2 x so that it has a denominator of ...
 7.7.7.8: Complete the table. r tdSnowmobile 44 4 truck r 5 3
 7.8: Simplify each rational expression, if possible. Assume that no deno...
 7.7.3.8: Factor each denominator completely. a. 1740x2b. x 252x2 6x1
 7.7.5.8: Fill in the blanks. a 1 5 1 a b a a 4 2 a b 20a 20a 1 5 ( ) 1 a ( )...
 7.7.2.8: Use the fact that 1 tablespoon = 3 to write two unit conversion fac...
 7.7.1.8: Simplify each expression. d. x xx x(x 30)
 7.7.6.9: By what should both sides of the equation be multiplied to clear it...
 7.7.8.9: Snacks. In a sample of 25 bags of potato chips, 2 were found to be ...
 7.7.4.9: Complete the solution. 2573x 25 3x73x 5x 6x35 6x 15x
 7.7.7.9: Complete the table. Rate Time Work completed1st printer2nd printer ...
 7.9: Simplify each rational expression, if possible. Assume that no deno...
 7.7.3.9: Consider the following factorizations. 18x 36 2 3 3 (x 2) 3x 6 3(x ...
 7.7.5.9: Simplify each complex fraction. See Example 1. 2334
 7.7.2.9: What units are common to the numerator and denominator of the follo...
 7.7.1.9: Complete the solution to simplify the rational expression. x2 2x 1x...
 7.7.6.10: By what should both sides of the equation be multiplied to clear it...
 7.7.8.10: Miniatures. A model of the Seattle Space Needle is to be made using...
 7.7.4.10: Are the students answers and the books answers equivalent? Students...
 7.7.7.10: Complete the table. P r tI City savings bank 1 50 Credit union r 0....
 7.10: Simplify each rational expression, if possible. Assume that no deno...
 7.7.3.10: Fill in the blanks. To write xx 9as an equivalent rational expressi...
 7.7.5.10: Simplify each complex fraction. See Example 1. 3527
 7.7.2.10: a. What fact is indicated by the unit conversion factor 1 day24 hou...
 7.7.1.10: In the following table, a students answers to three homework proble...
 7.7.6.11: Perform each multiplication. a. 4xa b 34xbb. (x 6)(x 2)a 3x 2a b 3
 7.7.8.11: Kleenex. Complete the following proportion that can be used to find...
 7.7.4.11: Perform the operations. Simplify, if possible. See Example 1. x32x7
 7.7.7.11: Write 559 days using a mixed number.
 7.11: Simplify each rational expression, if possible. Assume that no deno...
 7.7.3.11: Complete the solution. 6a 14a 12a 34a 1 6a 1 (2a )xx 9 8a4a 16a 2( ...
 7.7.5.11: Simplify each complex fraction. See Example 1. x265
 7.7.2.11: Multiply, and then simplify, if possible. See Example 1. 37 y2
 7.7.1.11: Evaluate each expression for x = 6. See Example 1. x 2x 5x
 7.7.6.12: Fill in the blanks. xa548xa b 18x 8xa
 7.7.8.12: The two triangles shown in the following illustration are similar. ...
 7.7.7.12: a. Write 9% as a decimal. b. Write 0.035 as a percent.
 7.7.4.12: Perform the operations. Simplify, if possible. See Example 1. y43y5
 7.12: Simplify each rational expression, if possible. Assume that no deno...
 7.7.3.12: The type of multiplication that is used to build rational expressio...
 7.7.5.12: Simplify each complex fraction. See Example 1. 947x
 7.7.2.12: Multiply, and then simplify, if possible. See Example 1. 27 z3
 7.7.1.12: Evaluate each expression for x = 6. See Example 1. 3x 2x 2x
 7.7.6.13: Complete the solution to solve the equation. a 4 a 4 7 aa2ab a12b a...
 7.7.8.13: Complete the solution. Solve for : 18x 288 18x
 7.7.7.13: Solve each of these number problems. See Example 1. If the same num...
 7.7.4.13: Perform the operations. Simplify, if possible. See Example 1. 7a84a5
 7.13: Explain the error in the following work: 1x x1 1x1 21 24(t
 7.7.3.13: Add and simplify the result, if possible. See Example 1. 9x2x
 7.7.5.13: Simplify each complex fraction. See Example 1. xy1x
 7.7.2.13: Multiply, and then simplify, if possible. See Example 1. y 2y 3y2
 7.7.1.13: Evaluate each expression for x = 6. See Example 1. x2 4x 12x2 x 23x
 7.7.1.14: Evaluate each expression for x = 6. See Example 1. x2 36x3 1x
 7.7.6.14: Can 5x12x 452be written as 5x 2x 45 5? Explain.
 7.7.8.14: Write the ratio of 25 to 4 in two other forms.
 7.7.7.14: Solve each of these number problems. See Example 1. If the same num...
 7.7.4.14: Perform the operations. Simplify, if possible. See Example 1. 5t64t7
 7.14: Dosages. Cowlings rule is a formula that can be used to determine t...
 7.7.3.14: Add and simplify the result, if possible. See Example 1. 4s4s
 7.7.5.14: Simplify each complex fraction. See Example 1. yxxxy
 7.7.2.14: Multiply, and then simplify, if possible. See Example 1. 4a 1 a7
 7.7.1.15: Evaluate each expression for x = 6. See Example 1. x 1x2 5x 6x
 7.7.6.15: Solve each equation and check the result. If an equation has no sol...
 7.7.8.15: Fill in the blanks: The proportion 201.6 1008 can be read: 20 is to...
 7.7.7.15: Solve each of these number problems. See Example 1. If the denomina...
 7.7.4.15: Perform the operations. Simplify, if possible. See Example 2. 7m2 2m
 7.15: Multiply and simplify, if possible. 3xy2x 4x2y2
 7.7.3.15: Add and simplify the result, if possible. See Example 1. x18518
 7.7.5.15: Simplify each complex fraction. See Example 1. n81n2
 7.7.2.15: Multiply, and then simplify, if possible. See Example 1. 35n12 167n2
 7.7.1.16: Evaluate each expression for x = 6. See Example 1. 2x2 3x 6x
 7.7.6.16: Solve each equation and check the result. If an equation has no sol...
 7.7.8.16: Fill in the blank: We read DXYZ DMNO X as: triangle XYZis ____ to t...
 7.7.7.16: Solve each of these number problems. See Example 1. If a number is ...
 7.7.4.16: Perform the operations. Simplify, if possible. See Example 2. 6n2 2n
 7.16: Multiply and simplify, if possible. 56xa127xb
 7.7.3.16: Add and simplify the result, if possible. See Example 1. 7103y10
 7.7.5.16: Simplify each complex fraction. See Example 1. mm315
 7.7.2.16: Multiply, and then simplify, if possible. See Example 1. 11m21 1455m3
 7.7.1.17: Evaluate each expression for . See Example 1. y 53y 2y
 7.7.6.17: Solve each equation and check the result. If an equation has no sol...
 7.7.8.17: Translate each ratio into a fraction in simplest form. See Example ...
 7.7.4.17: Perform the operations. Simplify, if possible. See Example 2. 35p2 ...
 7.7.7.17: Solve each of these number problems. See Example 1. If a number is ...
 7.17: Multiply and simplify, if possible. x2 1x2 2x xx 156
 7.7.3.17: Add and simplify the result, if possible. See Example 1. a 53a353a37
 7.7.5.17: Simplify each complex fraction. See Example 1. 4a116a455
 7.7.2.17: Multiply, and then simplify, if possible. See Example 1. 2x2y3xy 3xy22
 7.7.1.18: Evaluate each expression for . See Example 1. 2y 9y2 25y
 7.7.6.18: Solve each equation and check the result. If an equation has no sol...
 7.7.8.18: Translate each ratio into a fraction in simplest form. See Example ...
 7.7.4.18: Perform the operations. Simplify, if possible. See Example 2. 1516a...
 7.7.7.18: Solve each of these number problems. See Example 1. If a number is ...
 7.18: Multiply and simplify, if possible. x2 x3x 15 6x 30x2 2x 1x2
 7.7.3.18: Add and simplify the result, if possible. See Example 1. b3 810b481...
 7.7.5.18: Simplify each complex fraction. See Example 1. 1415m2125m6
 7.7.2.18: Multiply, and then simplify, if possible. See Example 1. 2x2zz 5xz
 7.7.1.19: Evaluate each expression for . See Example 1. yy2 y 62
 7.7.6.19: Solve each equation and check the result. If an equation has no sol...
 7.7.8.19: Translate each ratio into a fraction in simplest form. See Example ...
 7.7.4.19: Perform the operations. Simplify, if possible. See Example 2. 16t 1...
 7.7.7.19: Solve each of these number problems. See Example 1. The sum of a nu...
 7.19: Divide and simplify, if possible. 3x25x2y 6x15xy2
 7.7.3.19: Add and simplify the result, if possible. See Example 1. x 32y x 52yb3
 7.7.5.19: Simplify each complex fraction. See Example 1. x4307x215
 7.7.2.19: Multiply, and then simplify, if possible. See Example 2. x 55 xx 52
 7.7.1.20: Evaluate each expression for . See Example 1. y33y2 1 y
 7.7.6.20: Solve each equation and check the result. If an equation has no sol...
 7.7.8.20: Translate each ratio into a fraction in simplest form. See Example ...
 7.7.4.20: Perform the operations. Simplify, if possible. See Example 2. 310a ...
 7.7.7.20: Solve each of these number problems. See Example 1. The sum of the ...
 7.20: Divide and simplify, if possible. x2 x 61 2x x2 2x 32x2 x 1
 7.7.3.20: Add and simplify the result, if possible. See Example 1. y 210z y 4...
 7.7.5.20: Simplify each complex fraction. See Example 1. 5x224x556
 7.7.2.20: Multiply, and then simplify, if possible. See Example 2. a 99 8aa 9x
 7.7.1.21: Evaluate each expression for . See Example 1. y2 99 y2
 7.7.6.21: Solve each equation and check the result. If an equation has no sol...
 7.7.8.21: Translate each ratio into a fraction in simplest form. See Example ...
 7.7.4.21: Perform the operations. Simplify, if possible. See Example 2. 16c4 ...
 7.7.7.21: Cooking. If the same number is added to both the numerator and the ...
 7.21: Determine whether the given fraction is a unit conversion factor. a...
 7.7.3.21: Add and simplify the result, if possible. See Example 2. 2r2 3r 10 ...
 7.7.5.21: Simplify each complex fraction. See Examples 2 or 4. 12343214
 7.7.2.21: Multiply, and then simplify, if possible. See Example 2. 2x 6x 3 34xa
 7.7.1.22: Evaluate each expression for . See Example 1. y 11y2 2y 3y
 7.7.6.22: Solve each equation and check the result. If an equation has no sol...
 7.7.8.22: Translate each ratio into a fraction in simplest form. See Example ...
 7.7.4.22: Perform the operations. Simplify, if possible. See Example 2. 78b2 ...
 7.7.7.22: Tape Measures. If the same number is added to both the numerator an...
 7.22: Traffic Signs. Convert the speed limit on the sign from miles per h...
 7.7.3.22: Add and simplify the result, if possible. See Example 2. h2 4h 5hh2...
 7.7.5.22: Simplify each complex fraction. See Examples 2 or 4. 23 5223 32
 7.7.2.22: Multiply, and then simplify, if possible. See Example 2. 3y 9y 3 y3y22
 7.7.1.23: Find all real numbers for which the rational expression is undefine...
 7.7.6.23: Solve each equation and check the result. If an equation has no sol...
 7.7.8.23: Translate each ratio into a fraction in simplest form. See Example ...
 7.7.4.23: Perform the operations. Simplify, if possible. See Example 3. 2a 45...
 7.7.7.23: Tour De France. Maurice Garin of France won the first Tour de Franc...
 7.23: Add or subtract and simplify, if possible. 1315d 815d
 7.7.5.23: Simplify each complex fraction. See Examples 2 or 4. 141yy3 12
 7.7.3.23: Add and simplify the result, if possible. See Example 2. 3x 5x 26x ...
 7.7.2.23: Multiply, and then simplify, if possible. See Example 2. (x 1)2x 2 ...
 7.7.1.24: Find all real numbers for which the rational expression is undefine...
 7.7.6.24: Solve each equation and check the result. If an equation has no sol...
 7.7.8.24: Translate each ratio into a fraction in simplest form. See Example ...
 7.7.4.24: Perform the operations. Simplify, if possible. See Example 3. 5p2 9...
 7.7.7.24: Physical Fitness. A woman can bicycle 28 miles in the same time as ...
 7.24: Add or subtract and simplify, if possible. xx y yx y13
 7.7.5.24: Simplify each complex fraction. See Examples 2 or 4. 2x 1323 x5
 7.7.3.24: Add and simplify the result, if possible. See Example 2. 8x 7x 32x ...
 7.7.2.24: Multiply, and then simplify, if possible. See Example 2. (y 3)2y 5 ...
 7.7.1.25: Find all real numbers for which the rational expression is undefine...
 7.7.6.25: Solve each equation and check the result. If an equation has no sol...
 7.7.8.25: Translate each ratio into a fraction in simplest form. See Example ...
 7.7.4.25: Perform the operations. Simplify, if possible. See Example 3. 23a 2...
 7.7.7.25: Packaging Fruit. The diagram below shows how apples are processed f...
 7.25: Add or subtract and simplify, if possible. 3xx 7 x 2x 7
 7.7.5.25: Simplify each complex fraction. See Examples 2 or 4. 1y 523y
 7.7.2.25: Multiply, and then simplify, if possible. See Example 2. x2 xx 3x 6...
 7.7.3.25: Subtract and simplify the result, if possible. See Example 3. 2x25 x25
 7.7.1.26: Find all real numbers for which the rational expression is undefine...
 7.7.6.26: Solve each equation and check the result. If an equation has no sol...
 7.7.8.26: Translate each ratio into a fraction in simplest form. See Example ...
 7.7.4.26: Perform the operations. Simplify, if possible. See Example 3. 25b 3...
 7.7.7.26: Comparing Travel. A plane can fly 300 miles in the same time as it ...
 7.26: Add or subtract and simplify, if possible. aa2 2a 82a2 2a 8
 7.7.2.26: Multiply, and then simplify, if possible. See Example 2. 5z 10z 2 3...
 7.7.5.26: Simplify each complex fraction. See Examples 2 or 4. 16 5s2s
 7.7.3.26: Subtract and simplify the result, if possible. See Example 3. 16c11...
 7.7.1.27: Find all real numbers for which the rational expression is undefine...
 7.7.6.27: Solve each equation and check the result. If an equation has no sol...
 7.7.8.27: Translate each ratio into a fraction in simplest form. See Example ...
 7.7.4.27: Perform the operations. Simplify, if possible. See Example 3. 4a 2 ...
 7.7.7.27: Birds in Flight. Although flight speed is dependent upon the weathe...
 7.27: Find the LCD of each pair of rational expressions. 12x ,19
 7.7.2.27: Multiply, and then simplify, if possible. See Example 2. x2 x 65x 5...
 7.7.5.27: Simplify each complex fraction. See Examples 2 or 4. 4c c62c
 7.7.3.27: Subtract and simplify the result, if possible. See Example 3. m 16m...
 7.7.1.28: Find all real numbers for which the rational expression is undefine...
 7.7.6.28: Solve each equation and check the result. If an equation has no sol...
 7.7.8.28: Translate each ratio into a fraction in simplest form. See Example ...
 7.7.4.28: Perform the operations. Simplify, if possible. See Example 3. 9b2 2...
 7.7.7.28: Fast Cars. The top speed of a Dodge Charger SRT8 is 33 mph less tha...
 7.28: Find the LCD of each pair of rational expressions. 2x3, 58x
 7.7.2.28: Multiply, and then simplify, if possible. See Example 2. z2 4z 55z ...
 7.7.5.28: Simplify each complex fraction. See Examples 2 or 4. 10n n48n
 7.7.3.28: Subtract and simplify the result, if possible. See Example 3. c 74c...
 7.7.5.29: Simplify each complex fraction. See Examples 3 or 5. 23 113 11
 7.7.3.29: Subtract and simplify the result, if possible. See Example 3. tt2 t...
 7.7.1.29: Find all real numbers for which the rational expression is undefine...
 7.7.6.29: Solve each equation and check the result. If an equation has no sol...
 7.7.8.29: Determine whether each equation is a true proportion. See Example 2...
 7.7.4.29: Perform the operations. Simplify, if possible. See Example 3. 65m2 ...
 7.7.7.29: 9. Wind Speed. When a plane flies downwind, the wind pushes the pla...
 7.29: Find the LCD of each pair of rational expressions. 7m,m 2m 8
 7.7.2.29: Multiply, and then simplify, if possible. See Example 2. m2 2m 32m ...
 7.7.5.30: Simplify each complex fraction. See Examples 3 or 5. 35 225 2
 7.7.1.30: Find all real numbers for which the rational expression is undefine...
 7.7.3.30: Subtract and simplify the result, if possible. See Example 3. rr2 2...
 7.7.6.30: Solve each equation and check the result. If an equation has no sol...
 7.7.8.30: Determine whether each equation is a true proportion. See Example 2...
 7.7.4.30: Perform the operations. Simplify, if possible. See Example 3. 92c2 ...
 7.7.7.30: Boating. A boat that travels 18 mph in still water can travel 22 mi...
 7.30: Find the LCD of each pair of rational expressions. x5x 1, 5x5x 1
 7.7.2.30: Multiply, and then simplify, if possible. See Example 2. p2 p 63p 9...
 7.7.1.31: Find all real numbers for which the rational expression is undefine...
 7.7.5.31: Simplify each complex fraction. See Examples 3 or 5. 1x 35x 2
 7.7.3.31: Subtract and simplify the result, if possible. See Example 3. 11w 6...
 7.7.6.31: Solve each equation and check the result. If an equation has no sol...
 7.7.8.31: Determine whether each equation is a true proportion. See Example 2...
 7.7.4.31: Perform the operations. Simplify, if possible. See Example 4. 9t 38...
 7.7.7.31: Roofing Houses. A homeowner estimates that it will take her 7 days ...
 7.31: Find the LCD of each pair of rational expressions. 6 aa2 25, a2a 5
 7.7.2.31: Multiply, and then simplify, if possible. See Example 3. 7ma b 5mb
 7.7.1.32: Find all real numbers for which the rational expression is undefine...
 7.7.5.32: Simplify each complex fraction. See Examples 3 or 5. y 33y 2
 7.7.3.32: Subtract and simplify the result, if possible. See Example 3. y 82y...
 7.7.6.32: Solve each equation and check the result. If an equation has no sol...
 7.7.8.32: Determine whether each equation is a true proportion. See Example 2...
 7.7.4.32: Perform the operations. Simplify, if possible. See Example 4. 2m 37m 4
 7.7.7.32: Holiday Decorating. One crew can put up holiday decorations in the ...
 7.32: Find the LCD of each pair of rational expressions. 4t 25t2 10t 25, ...
 7.7.2.32: Multiply, and then simplify, if possible. See Example 3. 9pa10pa b 5
 7.7.1.33: Find all real numbers for which the rational expression is undefine...
 7.7.5.33: Simplify each complex fraction. See Examples 3 or 5. 2x24x25
 7.7.3.33: Subtract and simplify the result, if possible. See Example 4. 3y 22...
 7.7.6.33: Solve each equation and check the result. If an equation has no sol...
 7.7.8.33: Solve each proportion. See Example 3. 23 x6
 7.7.4.33: Perform the operations. Simplify, if possible. See Example 4. 3x2x ...
 7.7.7.33: Recreation Director Suppose you are a recreation director at a summ...
 7.33: Build each rational expression into an equivalent fraction having t...
 7.7.2.33: Multiply, and then simplify, if possible. See Example 3. 15xa b x 1...
 7.7.1.34: Find all real numbers for which the rational expression is undefine...
 7.7.5.34: Simplify each complex fraction. See Examples 3 or 5. 3x39x3
 7.7.3.34: Subtract and simplify the result, if possible. See Example 4. 5x 83...
 7.7.6.34: Solve each equation and check the result. If an equation has no sol...
 7.7.8.34: Solve each proportion. See Example 3. 36 x8
 7.7.4.34: Perform the operations. Simplify, if possible. See Example 4. 2y5y ...
 7.7.7.34: Groundskeeping. It takes a groundskeeper 45 minutes to prepare a so...
 7.34: Build each rational expression into an equivalent fraction having t...
 7.7.2.34: Multiply, and then simplify, if possible. See Example 3. 30tat 710t...
 7.7.1.35: Find all real numbers for which the rational expression is undefine...
 7.7.5.35: Simplify each complex fraction. See Examples 3 or 5. 3yxyyyx
 7.7.3.35: Subtract and simplify the result, if possible. See Example 4. 6x23x...
 7.7.6.35: Solve each equation and check the result. If an equation has no sol...
 7.7.8.35: Solve each proportion. See Example 3. 63g 92
 7.7.4.35: Perform the operations. Simplify, if possible. See Example 4. s 7s ...
 7.7.7.35: Filling a Pool. One inlet pipe can fill an empty pool in 4 hours, a...
 7.35: Build each rational expression into an equivalent fraction having t...
 7.7.2.35: Multiply, and then simplify, if possible. See Example 3. 12ya b 5y ...
 7.7.1.36: Find all real numbers for which the rational expression is undefine...
 7.7.5.36: Simplify each complex fraction. See Examples 3 or 5. yx3yy2yx3
 7.7.3.36: Subtract and simplify the result, if possible. See Example 4. 8a22a...
 7.7.6.36: Solve each equation and check the result. If an equation has no sol...
 7.7.8.36: Solve each proportion. See Example 3. 27x 94
 7.7.4.36: Perform the operations. Simplify, if possible. See Example 4. t 5t ...
 7.7.7.36: Sewage Treatment. A sludge pool is filled by two inlet pipes. One p...
 7.36: Build each rational expression into an equivalent fraction having t...
 7.7.2.36: Multiply, and then simplify, if possible. See Example 3. 16xa3x 84x...
 7.7.1.37: Find all real numbers for which the rational expression is undefine...
 7.7.5.37: Simplify each complex fraction. See Example 4. 162x161x
 7.7.3.37: Subtract and simplify the result, if possible. See Example 4. 6x 53...
 7.7.6.37: Solve each equation and check the result. If an equation has no sol...
 7.7.8.37: Solve each proportion. See Example 3. x 15 3152
 7.7.4.37: Perform the operations. Simplify, if possible. See Example 4. 3mm 2...
 7.7.7.37: On average, it takes a teacher 30 minutes to grade a set of quizzes...
 7.37: Add or subtract and simplify, if possible. 17 1a
 7.7.2.37: Multiply, and then simplify, if possible. See Example 3. 24a b 3a 5...
 7.7.1.38: Find all real numbers for which the rational expression is undefine...
 7.7.5.38: Simplify each complex fraction. See Example 4. 341y561y
 7.7.3.38: Subtract and simplify the result, if possible. See Example 4. 7x 75...
 7.7.6.38: Solve each equation and check the result. If an equation has no sol...
 7.7.8.38: Solve each proportion. See Example 3. x 17 221
 7.7.4.38: Perform the operations. Simplify, if possible. See Example 4. 2xx 2...
 7.38: Add or subtract and simplify, if possible. xx 11x
 7.7.2.38: Multiply, and then simplify, if possible. See Example 3. 28a8 3t4ta...
 7.7.7.38: Dog Kennels. It takes the owner/operator of a dog kennel 6 hours to...
 7.7.7.39: Printers. It takes a printer 6 hours to print the class schedules f...
 7.7.1.39: Simplify. See Example 3. 459a
 7.7.5.39: Simplify each complex fraction. See Example 4. a77a1a17
 7.7.3.39: Subtract and simplify the result, if possible. See Example 4. 2 pp2...
 7.7.6.39: Solve each equation and check the result. If an equation has no sol...
 7.7.8.39: Solve each proportion. See Example 3. 5 x17 1334
 7.7.4.39: Perform the operations. Simplify, if possible. See Example 5. 4s2 5...
 7.39: Add or subtract and simplify, if possible. 2t 2t2 2t 1 1t 1x
 7.7.2.39: Divide, and then simplify, if possible. See Example 4. 2y 43
 7.7.7.40: Office Work. In 5 hours, a secretary can address 100 envelopes. Ano...
 7.7.1.40: Simplify. See Example 3. 4816y
 7.7.5.40: Simplify each complex fraction. See Example 4. t99t1t19
 7.7.3.40: Subtract and simplify the result, if possible. See Example 4. 2 7nn...
 7.7.6.40: Solve each equation and check the result. If an equation has no sol...
 7.7.8.40: Solve each proportion. See Example 3. 4 x13 1126
 7.7.4.40: Perform the operations. Simplify, if possible. See Example 5. dd2 6...
 7.40: Add or subtract and simplify, if possible. x 22x 2 xx2
 7.7.2.40: Divide, and then simplify, if possible. See Example 4. 3a 95
 7.7.7.41: Comparing Investments. An amount of money invested for 1 year in ta...
 7.7.1.41: Simplify. See Example 3. 6x44x2
 7.7.5.41: Simplify each complex fraction. See Example 5. d244d5d12t
 7.7.3.41: Find the LCD of each pair of rational expressions. See Example 5. 1...
 7.7.6.41: Solve each equation and check the result. If an equation has no sol...
 7.7.8.41: Solve each proportion. See Example 3. 157b 5 52b 14
 7.7.4.41: Perform the operations. Simplify, if possible. See Example 5. 5x2 9...
 7.41: Add or subtract and simplify, if possible. 6b 1 b1 b
 7.7.2.41: Divide, and then simplify, if possible. See Example 4. 3a25 15
 7.7.2.42: Divide, and then simplify, if possible. See Example 4. 3y8 32
 7.7.7.42: Comparing Investments. An amount of money invested for 1 year in a ...
 7.7.1.42: Simplify. See Example 3. 9x36x
 7.7.5.42: Simplify each complex fraction. See Example 5. d22d3d4
 7.7.3.42: Find the LCD of each pair of rational expressions. See Example 5. 4...
 7.7.6.42: Solve each equation and check the result. If an equation has no sol...
 7.7.8.42: Solve each proportion. See Example 3. 83n 6 163n 31
 7.7.4.42: Perform the operations. Simplify, if possible. See Example 5. 3t2 t...
 7.42: Add or subtract and simplify, if possible. 8c 6
 7.7.2.43: Divide, and then simplify, if possible. See Example 4. x318y x6y
 7.7.7.43: Comparing Investments. Two certificates of deposit (CDs) pay intere...
 7.7.1.43: Simplify. See Example 4. 6x 39
 7.7.5.43: Simplify each complex fraction. See Example 5. 2x2y4x
 7.7.3.43: Find the LCD of each pair of rational expressions. See Example 5. 3...
 7.7.6.43: Solve each equation and check the result. If an equation has no sol...
 7.7.8.43: Solve each proportion. See Example 3. 8x3 11x 948
 7.7.4.43: Perform the operations. Simplify, if possible. See Example 5. 2a2 4...
 7.43: Add or subtract and simplify, if possible. n 7n 3 n 3n 78
 7.7.2.44: Divide, and then simplify, if possible. See Example 4. 21xz2 7x3z5
 7.7.7.44: Comparing Interest Rates. Two bond funds pay interest at rates that...
 7.7.1.44: Simplify. See Example 4. 4x 1216
 7.7.5.44: Simplify each complex fraction. See Example 5. 2y32y38y
 7.7.3.44: Find the LCD of each pair of rational expressions. See Example 5. m...
 7.7.6.44: Solve each equation and check the result. If an equation has no sol...
 7.7.8.44: Solve each proportion. See Example 3. 3x16 x 258
 7.7.4.44: Perform the operations. Simplify, if possible. See Example 5. c 64c...
 7.44: Add or subtract and simplify, if possible. 4t 2 7(t 2)2n
 7.45: Add or subtract and simplify, if possible. 6a2 9 5a2 a 6
 7.7.2.45: Divide, and then simplify, if possible. See Example 4. 27p435q 9p21q
 7.7.7.45: In Example 4, one inlet pipe could fill an oil tank in 7 days, and ...
 7.7.1.45: Simplify. See Example 4. x 33x 94
 7.7.5.45: Simplify each complex fraction. See Example 6. x111x12y
 7.7.3.45: Find the LCD of each pair of rational expressions. See Example 5. 3...
 7.7.6.45: Solve each equation and check the result. If an equation has no sol...
 7.7.8.45: Solve each proportion. See Example 4. 23x x6
 7.7.4.45: Perform the operations. Simplify, if possible. See Example 5. y2 16...
 7.46: Add or subtract and simplify, if possible. 23y 634y 8
 7.7.2.46: Divide, and then simplify, if possible. See Example 4. 1225s5 1015s2
 7.7.7.46: Write a sharedwork problem that can be modeled by the equation:x3 ...
 7.7.1.46: Simplify. See Example 4. 2x 14x 7x
 7.7.5.46: Simplify each complex fraction. See Example 6. 1x111x1
 7.7.3.46: Find the LCD of each pair of rational expressions. See Example 5. 2...
 7.7.6.46: Solve each equation and check the result. If an equation has no sol...
 7.7.8.46: Solve each proportion. See Example 4. y4 4y
 7.7.4.46: Perform the operations. Simplify, if possible. See Example 5. 6s2 9...
 7.47: Working on a homework assignment, a student added two rational expr...
 7.7.2.47: Divide, and then simplify, if possible. See Example 5. 9a 1828 9a335
 7.7.7.47: Solve using substitution: ex y 4y 3xx
 7.7.1.47: Simplify. See Example 4. x2 4x2 6x 82x
 7.7.5.47: Simplify each complex fraction. See Example 6. x2xx2x1
 7.7.3.47: Find the LCD of each pair of rational expressions. See Example 5. 8...
 7.7.6.47: Solve each formula for the specified variable. See Example 6. h 2Ab...
 7.7.8.47: Solve each proportion. See Example 4. b 53 2b
 7.7.4.47: Perform the operations. Simplify, if possible.See Example 6. 9yx 4 y6
 7.48: Digital Video Cameras. Find the perimeter and the area of the LED s...
 7.7.2.48: Divide, and then simplify, if possible. See Example 5. 3x 640 3x224
 7.7.7.48: Solve using elimination (addition): e5x 4y 193x 2y 7e
 7.7.1.48: Simplify. See Example 4. y2 25y2 3y 10x
 7.7.5.48: Simplify each complex fraction. See Example 6. 2x22x21
 7.7.3.48: Find the LCD of each pair of rational expressions. See Example 5. d...
 7.7.6.48: Solve each formula for the specified variable. See Example 6. T R3R...
 7.7.8.48: Solve each proportion. See Example 4. 2q q 32
 7.7.4.48: Perform the operations. Simplify, if possible.See Example 6. 9nm 4 ...
 7.49: Simplify each complex fraction. n4307n15
 7.7.2.49: Divide, and then simplify, if possible. See Example 5. x2 43x 6 2 x...
 7.7.7.49: Use a check to determine whether 215 is a solution of: x 20 4x 1 2x21
 7.7.1.49: Simplify. See Example 4. x2 5x 4x2 4xy
 7.7.5.49: Simplify each complex fraction. 1p1q1p
 7.7.6.49: Solve each formula for the specified variable. See Example 6. I r E...
 7.7.3.49: Find the LCD of each pair of rational expressions. See Example 6. 3...
 7.7.8.49: Solve each proportion. See Example 4. a 4a 15a 42
 7.7.4.49: Perform the operations. Simplify, if possible.See Example 6. 8x z
 7.50: Simplify each complex fraction. r2 8118s24r 369s
 7.7.2.50: Divide, and then simplify, if possible. See Example 5. x2 95x 15 3 ...
 7.7.7.50: Solve: 4x2 8x 0
 7.7.1.50: Simplify. See Example 4. x2 10x 21x2 3xx2
 7.7.5.50: Simplify each complex fraction. mn11mn
 7.7.3.50: Find the LCD of each pair of rational expressions. See Example 6. b...
 7.7.6.50: Solve each formula for the specified variable. See Example 6. Sk hI...
 7.7.8.50: Solve each proportion. See Example 4. ss 5 s 524a
 7.7.4.50: Perform the operations. Simplify, if possible.See Example 6. 2y z 8
 7.51: Simplify each complex fraction. 1y 11y 1r
 7.7.2.51: Divide, and then simplify, if possible. See Example 5. x2 7x5x 10 (...
 7.7.7.51: River Tours. A river boat tour begins by going 60 miles upstream ag...
 7.7.1.51: Simplify. See Example 5. m2 2mn n27m2 7n2x2
 7.7.5.51: Simplify each complex fraction. 40x220x9
 7.7.3.51: Find the LCD of each pair of rational expressions. See Example 6. b...
 7.7.8.51: Solve each proportion. See Example 4. t 3t 5 12t58
 7.7.6.51: Solve each formula for the specified variable. See Example 6. 5x 4y...
 7.7.4.51: Perform the operations. Simplify, if possible. See Example 7. 7a 454 a
 7.52: Simplify each complex fraction. 7a21a103
 7.7.2.52: Divide, and then simplify, if possible. See Example 5. x2 10x7x 7 (...
 7.7.7.52: Travel Time. A company president flew 680 miles one way in the corp...
 7.7.1.52: Simplify. See Example 5. 11c2 11d2c2 2cd d2m2
 7.7.5.52: Simplify each complex fraction. 18n26n13
 7.7.3.52: Find the LCD of each pair of rational expressions. See Example 6. b...
 7.7.8.52: Solve each proportion. See Example 4. 5h14h 3 1ht
 7.7.6.52: Solve each formula for the specified variable. See Example 6. 2c2d ...
 7.7.4.52: Perform the operations. Simplify, if possible. See Example 7. 4b 6b6 b
 7.53: Simplify each complex fraction. 2x 1 x 1x 11x2 1S
 7.7.2.53: Divide, and then simplify, if possible. See Example 5. m2 m 20m 4 mmx2
 7.7.7.53: Sales. A dealer bought some radios for a total of $1,200. She gave ...
 7.7.1.53: Simplify. See Example 5. 4b2 4b 1(2b 1)311
 7.7.5.53: Simplify each complex fraction. 1c121c214
 7.7.3.53: Find the LCD of each pair of rational expressions. See Example 6. 6...
 7.7.8.53: Each pair of triangles is similar. Find the missing side length. Se...
 7.7.6.53: Solve each formula for the specified variable. See Example 6. 1r1s ...
 7.7.4.53: Perform the operations. Simplify, if possible. See Example 7. c7c d...
 7.54: Simplify each complex fraction. 1x2y 5xy3xy 7xy2
 7.7.2.54: Divide, and then simplify, if possible. See Example 5. n2 4n 21n 3 ...
 7.7.7.54: Furnace Repairs. A repairman purchased several furnaceblower motors...
 7.7.1.54: Simplify. See Example 5. 9y2 12y 4(3y 2)34b
 7.7.5.54: Simplify each complex fraction. 1m1nmnnm
 7.7.3.54: Find the LCD of each pair of rational expressions. See Example 6. 5...
 7.7.8.54: Each pair of triangles is similar. Find the missing side length. Se...
 7.7.6.54: Solve each formula for the specified variable. See Example 6. 1x 1y...
 7.7.4.54: Perform the operations. Simplify, if possible. See Example 7. a5a 3...
 7.55: Solve each equation and check the result. If an equation has no sol...
 7.7.2.55: Divide, and then simplify, if possible. See Example 5. t2 5t 14t t ...
 7.7.1.55: Simplify. See Example 6. 10(c 3) 103(c 3) 39y
 7.7.5.55: Simplify each complex fraction. r113r111m
 7.7.3.55: Find the LCD of each pair of rational expressions. See Example 6. 2...
 7.7.8.55: Each pair of triangles is similar. Find the missing side length. Se...
 7.7.6.55: Solve each formula for the specified variable. See Example 7. Pn rt...
 7.7.4.55: Perform the operations and simplify, if possible. x 7x2 4x 5 x 9x2 ...
 7.56: Solve each equation and check the result. If an equation has no sol...
 7.7.2.56: Divide, and then simplify, if possible. See Example 5. r2 12r 11r r...
 7.7.1.56: Simplify. See Example 6. 6(d 3) 67(d 3) 710(
 7.7.5.56: Simplify each complex fraction. 51n742n71
 7.7.3.56: Find the LCD of each pair of rational expressions. See Example 6. 7...
 7.7.8.56: Each pair of triangles is similar. Find the missing side length. Se...
 7.7.6.56: Solve each formula for the specified variable. See Example 7. Fm P ...
 7.7.4.56: Perform the operations and simplify, if possible. rr2 5r 6 2r2 3r 2x
 7.57: Solve each equation and check the result. If an equation has no sol...
 7.7.2.57: Divide, and then simplify, if possible. See Example 5. x2 2x 353x2 ...
 7.7.1.57: Simplify. See Example 6. 6(x 3) 183x 186(
 7.7.5.57: Simplify each complex fraction. b2 8118a24b 36 9a
 7.7.3.57: Find the LCD of each pair of rational expressions. See Example 6. 4...
 7.7.8.57: Solve each proportion. x 1x 1 23xx
 7.7.6.57: Solve each formula for the specified variable. See Example 7. ab cd...
 7.7.4.57: Perform the operations and simplify, if possible. 3d 3d 9 3d9 d
 7.58: Solve each equation and check the result. If an equation has no sol...
 7.7.2.58: Divide, and then simplify, if possible. See Example 5. x2 x 62x2 9x...
 7.7.1.58: Simplify. See Example 6. 4(t 1) 44t 46(
 7.7.5.58: Simplify each complex fraction. 8x 64 yx2 64 y2
 7.7.3.58: Find the LCD of each pair of rational expressions. See Example 6. 4...
 7.7.8.58: Solve each proportion. 2x 6 2x5x
 7.7.6.58: Solve each formula for the specified variable. See Example 7. pcs t...
 7.7.4.58: Perform the operations and simplify, if possible. 2x 2x 2 2x2 x
 7.59: Solve each equation and check the result. If an equation has no sol...
 7.7.2.59: Divide, and then simplify, if possible. See Example 6. x2 13x 3 (x 1)x
 7.7.1.59: Simplify. See Example 7. 2x 77 2x4
 7.7.5.59: Simplify each complex fraction. 10xx36x3
 7.7.3.59: Find the LCD of each pair of rational expressions. See Example 6. 5...
 7.7.8.59: Solve each proportion. x 14 3x82
 7.7.6.59: Solve each formula for the specified variable. See Example 7. 1a1b ...
 7.7.4.59: Perform the operations and simplify, if possible. 10x 1 y
 7.60: Solve each equation and check the result. If an equation has no sol...
 7.7.2.60: Divide, and then simplify, if possible. See Example 6. x2 16x 4 (3x...
 7.7.1.60: Simplify. See Example 7. 18 dd 182
 7.7.5.60: Simplify each complex fraction. 18aa412a4
 7.7.3.60: Find the LCD of each pair of rational expressions. See Example 6. 4...
 7.7.8.60: Solve each proportion. x 19 2x3
 7.7.6.60: Solve each formula for the specified variable. See Example 7. 1a 1b...
 7.7.4.60: Perform the operations and simplify, if possible. 3s 8 t1
 7.61: Engineering. The efficiency of a Carnot engine is given by the foll...
 7.7.2.61: Divide, and then simplify, if possible. See Example 6. n2 10n 9n 9 ...
 7.7.1.61: Simplify. See Example 7. 3 4t8t 61
 7.7.5.61: Simplify each complex fraction. 418h1234h
 7.7.3.61: Build each rational expression into an equivalent expression with t...
 7.7.8.61: Solve each proportion. y 4y 1 y 3y 6x
 7.7.6.61: Solve each formula for the specified variable. See Example 7. F L26...
 7.7.4.61: Perform the operations and simplify, if possible. bb 1 b 1b 23
 7.62: Solve for : 1x 1y1z y
 7.7.2.62: Divide, and then simplify, if possible. See Example 6. r2 11r 18r 9...
 7.7.1.62: Simplify. See Example 7. 5t 13 15
 7.7.5.62: Simplify each complex fraction. 1213b121b2
 7.7.3.62: Build each rational expression into an equivalent expression with t...
 7.7.8.62: Solve each proportion .r 6r 8 r 1r 4y
 7.7.6.62: Solve each formula for the specified variable. See Example 7. H J 3...
 7.7.4.62: Perform the operations and simplify, if possible. xx 2 x 2x 3b
 7.63: Number Problems. If a number is subtracted from the denominator of ...
 7.7.2.63: Divide, and then simplify, if possible. See Example 6. 2r 3s12 (4r2...
 7.7.1.63: Simplify. See Example 8. 2 aa2 a 2
 7.7.5.63: Simplify each complex fraction. mnnmmnnm
 7.7.3.63: Build each rational expression into an equivalent expression with t...
 7.7.8.63: Solve each proportion. c10 10c
 7.7.6.63: Solve each equation and check the result. If an equation has no sol...
 7.7.4.63: Perform the operations and simplify, if possible. gg2 424 g2
 7.64: Exercise. A woman can bicycle 30 miles in the same time that it tak...
 7.7.2.64: Divide, and then simplify, if possible. See Example 6. 3m n18 (9m2 ...
 7.7.1.64: Simplify. See Example 8. 4 bb2 5b 42
 7.7.5.64: Simplify each complex fraction. 2abba2abba
 7.7.3.64: Build each rational expression into an equivalent expression with t...
 7.7.8.64: Solve each proportion. 6r r6
 7.7.4.64: Perform the operations and simplify, if possible. hh2 49749 h2
 7.7.6.64: Solve each equation and check the result. If an equation has no sol...
 7.65: House Cleaning. A maid can clean a house in 4 hours. What is her ra...
 7.7.2.65: Divide, and then simplify, if possible. See Example 6. 24n2 18n3n 1
 7.7.1.65: Simplify. See Example 8. 25 5mm2 254
 7.7.5.65: Simplify each complex fraction. 2c21c54
 7.7.3.65: Build each rational expression into an equivalent expression with t...
 7.7.8.65: Solve each proportion. m3 4m 1
 7.7.4.65: Perform the operations and simplify, if possible. 5y65y3
 7.7.6.65: Solve each equation and check the result. If an equation has no sol...
 7.66: House Painting. If a homeowner can paint a house in 14 days and a p...
 7.7.2.66: Divide, and then simplify, if possible. See Example 6. 2m 16m2m 4
 7.7.1.66: Simplify. See Example 8. 36 6hh2 362
 7.7.5.66: Simplify each complex fraction. 7s21s103
 7.7.3.66: Build each rational expression into an equivalent expression with t...
 7.7.8.66: Solve each proportion. n2 5n 3m
 7.7.4.66: Perform the operations and simplify, if possible. 4x3 x6
 7.7.6.66: Solve each equation and check the result. If an equation has no sol...
 7.7.4.67: Perform the operations and simplify, if possible. 15x7xx 54
 7.67: Investments. In 1 year, a student earned $100 interest on money she...
 7.7.2.67: Complete each unit conversion. See Examples 7 and 8. 150 yards1 3 f...
 7.7.1.67: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.67: Simplify each complex fraction. 4t8t28t 16 t5
 7.7.3.67: Build each rational expression into an equivalent expression with t...
 7.7.8.67: Solve each proportion. 33b 4 25b 6n
 7.7.6.67: Solve each equation and check the result. If an equation has no sol...
 7.7.4.68: Perform the operations and simplify, if possible. 10hh 379h
 7.68: Wind Speed. A plane flies 400 miles downwind in the same amount of ...
 7.7.2.68: Complete each unit conversion. See Examples 7 and 8. 60 inches1 1 f...
 7.7.1.68: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.68: Simplify each complex fraction. 9m 27 m62m6m8
 7.7.3.68: Build each rational expression into an equivalent expression with t...
 7.7.8.68: Solve each proportion. 24d 1 32d 13
 7.7.6.68: Solve each equation and check the result. If an equation has no sol...
 7.7.4.69: Perform the operations and simplify, if possible. 115x 56x
 7.69: Determine whether each equation is a proportion. 47 2034
 7.7.2.69: Complete each unit conversion. See Examples 7 and 8. 6 pints1 1gall...
 7.7.1.69: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.69: Simplify each complex fraction. 2s2s24s34s2
 7.7.3.69: Build each rational expression into an equivalent expression with t...
 7.7.8.69: Solve each equation. a. 2 5 3 4x b. 4x 25 34x
 7.7.6.69: Solve each equation and check the result. If an equation has no sol...
 7.7.4.70: Perform the operations and simplify, if possible. 59y 14y
 7.70: Determine whether each equation is a proportion. 57 3042
 7.7.2.70: Complete each unit conversion. See Examples 7 and 8. 4 cups1 1gallo...
 7.7.1.70: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.70: Simplify each complex fraction. 2x32x4x8x2
 7.7.3.70: Build each rational expression into an equivalent expression with t...
 7.7.8.70: Solve each equation. a. 14 23ab. 56a14 23a1
 7.7.6.70: Solve each equation and check the result. If an equation has no sol...
 7.7.6.71: Solve each equation and check the result. If an equation has no sol...
 7.7.4.71: Perform the operations and simplify, if possible. xx 1 x 1x5
 7.71: Solve each proportion. 3x 69
 7.7.2.71: Complete each unit conversion. See Examples 7 and 8. 30 miles1 hour...
 7.7.1.71: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.71: Simplify each complex fraction. 16t8t211t 12t22
 7.7.3.71: Build each rational expression into an equivalent expression with t...
 7.7.8.71: Solve each equation. a. 3a 1 8ab. 3a 18a 33
 7.7.6.72: Solve each equation and check the result. If an equation has no sol...
 7.72: Solve each proportion. x3 x5
 7.7.4.72: Perform the operations and simplify, if possible. t 2ttt 3x
 7.7.2.72: Complete each unit conversion. See Examples 7 and 8. 300 meters3 mo...
 7.7.1.72: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.72: Simplify each complex fraction. 1p2p6p21p11
 7.7.3.72: Build each rational expression into an equivalent expression with t...
 7.7.8.72: Solve each equation. a. 43x 13b. 43x 13 x
 7.7.6.73: Solve each equation and check the result. If an equation has no sol...
 7.73: Solve each proportion. x 25 x7
 7.7.4.73: Perform the operations and simplify, if possible. yy 1 41 y
 7.7.2.73: Complete each unit conversion. See Examples 7 and 8. 30 meters1 sec...
 7.7.1.73: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.73: Simplify each complex fraction. 1x1y
 7.7.3.73: Build each rational expression into an equivalent expression with t...
 7.7.8.73: Shopping for Clothes. If shirts are on sale at two for $25, how muc...
 7.7.6.74: Solve each equation and check the result. If an equation has no sol...
 7.74: Solve each proportion. 2xx 4 3x 1x
 7.7.4.74: Perform the operations and simplify, if possible. t 7 t7 t
 7.7.2.74: Complete each unit conversion. See Examples 7 and 8. 288 inches21 y...
 7.7.1.74: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.74: Simplify each complex fraction. baab
 7.7.3.74: Build each rational expression into an equivalent expression with t...
 7.7.8.74: Mixing Perfume. A perfume is to be mixed in the ratio of 3 drops of...
 7.7.6.75: Solve each equation and check the result. If an equation has no sol...
 7.75: Dentistry. The diagram in the next column was displayed in a dentis...
 7.7.4.75: Perform the operations and simplify, if possible. n5 n 215
 7.7.2.75: Perform the operations and simplify, if possible. b2 5b 6b2 10b 16 ...
 7.7.1.75: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.75: Simplify each complex fraction. 2516x21532x
 7.7.3.75: Build each rational expression into an equivalent expression with t...
 7.7.8.75: CPR. A first aid handbook states that when performing cardiopulmona...
 7.7.6.76: Solve each equation and check the result. If an equation has no sol...
 7.76: Utility Poles. A telephone pole casts a shadow 12 feet long at the ...
 7.7.4.76: Perform the operations and simplify, if possible. m9 m 127
 7.7.2.76: Perform the operations and simplify, if possible. m2 m 6m2 6m 9 m2 ...
 7.7.1.76: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.76: Simplify each complex fraction. 21 8g3 3516g8
 7.7.3.76: Build each rational expression into an equivalent expression with t...
 7.7.8.76: Cooking. A recipe for wild rice soup follows. Find the amounts of c...
 7.7.6.77: Solve each equation and check the result. If an equation has no sol...
 7.77: Porcelain Figurines. A model of a flutist, standing and playing at ...
 7.7.4.77: Perform the operations and simplify, if possible. y 25y2 y 415ym
 7.7.2.77: Perform the operations and simplify, if possible. 5x 525 5(x 1)3m
 7.7.1.77: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.77: Simplify each complex fraction. 33x133x1
 7.7.3.77: Perform the operations. Then simplify, if possible. 3tt2 8t 7 3t2 8...
 7.7.8.77: Recreation Director A total of 966 boys and girls are members of a ...
 7.7.6.78: Solve each equation and check the result. If an equation has no sol...
 7.78: Comparison Shopping. Which is the better buy for recordable compact...
 7.7.2.78: Perform the operations and simplify, if possible. 7t 728 4(t 1)45
 7.7.4.78: Perform the operations and simplify, if possible. x 3x2 x 52xy
 7.7.1.78: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.78: Simplify each complex fraction. 22x122x13
 7.7.3.78: Perform the operations. Then simplify, if possible. 10xx2 2x 1 10x2...
 7.7.8.78: Gear Ratios. Write each ratio in two ways: as a fraction in simples...
 7.7.8.79: Computing a Paycheck. Billie earns $412 for a 40hour week. If she ...
 7.7.6.79: Solve each equation and check the result. If an equation has no sol...
 7.7.2.79: Perform the operations and simplify, if possible. 6a2a2 6a 9 (a 3)4...
 7.7.4.79: Perform the operations and simplify, if possible. xx 24 2xx2 4x
 7.7.1.79: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.79: Simplify each complex fraction. 19d226d
 7.7.3.79: Perform the operations. Then simplify, if possible. cc2 d2 dc2 d210
 7.7.8.80: Waves. If the peak height to wavelength ratio is greater than 1:7, ...
 7.7.6.80: Solve each equation and check the result. If an equation has no sol...
 7.7.2.80: Perform the operations and simplify, if possible. 9b3b2 8b 16 (b 4)...
 7.7.4.80: Perform the operations and simplify, if possible. yy 3 2y 6y2 9
 7.7.1.80: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.80: Simplify each complex fraction. 1 16a212a3
 7.7.3.80: Perform the operations. Then simplify, if possible. bb2 4 2b2 4c
 7.7.8.81: Twitter. According to a June, 2010 article in the Blog Herald, appr...
 7.7.6.81: Solve each equation and check the result. If an equation has no sol...
 7.7.2.81: Perform the operations and simplify, if possible. 36c2 49d23d3 12c ...
 7.7.4.81: Perform the operations and simplify, if possible. b 3a2
 7.7.1.81: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.81: Simplify each complex fraction. a2b5ab3ab7ab2
 7.7.3.81: Perform the operations. Then simplify, if possible. a2 a4a2 8a2a2 7...
 7.7.8.82: Engineering. A portion of a bridge is shown. Use the fact that is i...
 7.7.6.82: Solve each equation and check the result. If an equation has no sol...
 7.7.2.82: Perform the operations and simplify, if possible. 25y2 16z22yz 10y ...
 7.7.4.82: Perform the operations and simplify, if possible. c 53b
 7.7.1.82: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.82: Simplify each complex fraction. 3ab26a2b6a9b2
 7.7.3.82: Perform the operations. Then simplify, if possible. b2 16b6b2 9b7b2...
 7.7.8.83: Nutrition. The table shows the nutritional facts about a 10oz choc...
 7.7.6.83: Solve each equation and check the result. If an equation has no sol...
 7.7.2.83: Perform the operations and simplify, if possible. 10ha b 5h 32h b2
 7.7.4.83: Perform the operations and simplify, if possible. 73a1a 2
 7.7.1.83: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.83: Simplify each complex fraction. m 12m 11 m2m 18
 7.7.3.83: Perform the operations. Then simplify, if possible. 17a2a 4 7a2a 43b
 7.7.8.84: Photo Enlargements. The 3by5 photo is to be blown up to the large...
 7.7.6.84: Solve each equation and check the result. If an equation has no sol...
 7.7.2.84: Perform the operations and simplify, if possible. 33ra5r 411r a b 5h
 7.7.4.84: Perform the operations and simplify, if possible. 59x4x 67
 7.7.1.84: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.84: Simplify each complex fraction. 1 r2r 1r 12r 1m
 7.7.3.84: Perform the operations. Then simplify, if possible.10b3b 18 4b3b 1817a
 7.7.8.85: Mixing Fuel. The instructions on a can of oil intended to be added ...
 7.7.6.85: Solve each equation and check the result. If an equation has no sol...
 7.7.2.85: Perform the operations and simplify, if possible. n2 9n2 3n n 3n2 n103
 7.7.4.85: Perform the operations and simplify, if possible. 3x217x
 7.7.1.85: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.85: Slope. We can use the slope formula shown below to find the slope o...
 7.7.3.85: Perform the operations. Then simplify, if possible. 89 3x2 6x 89 3x...
 7.7.8.86: Drivers Licenses. Of the 50 states, Alabama has one of the highest ...
 7.7.6.86: Solve each equation and check the result. If an equation has no sol...
 7.7.2.86: Perform the operations and simplify, if possible. b2 bb 2 b2 2bb2 4n2
 7.7.4.86: Perform the operations and simplify, if possible. 7c14c2
 7.7.1.86: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.86: Pitching. The earned run average (ERA) is a statistic that gives th...
 7.7.3.86: Perform the operations. Then simplify, if possible. 510 5t2 15t 510...
 7.7.8.87: CaptureRelease Method. To estimate the ground squirrel population o...
 7.7.6.87: Solve each equation and check the result. If an equation has no sol...
 7.7.2.87: Perform the operations and simplify, if possible. 0r2s6rs2 3r32rs
 7.7.4.87: Perform the operations and simplify, if possible. x 2x 1 57
 7.7.1.87: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.87: Electronics. In electronic circuits, resistors are tiny components ...
 7.7.3.87: Perform the operations. Then simplify, if possible. 11n(n 4)(n 2) 4...
 7.7.8.88: Concrete. A 2:3 concrete mix means that for every two parts of sand...
 7.7.6.88: Solve each equation and check the result. If an equation has no sol...
 7.7.2.88: Perform the operations and simplify, if possible. 3a3b25cd3 5cd26ab
 7.7.4.88: Perform the operations and simplify, if possible. y 8y 8 4 x
 7.7.1.88: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.5.88: Data Analysis. Use the data in the table to find the average measur...
 7.7.3.88: Perform the operations. Then simplify, if possible. (t 1)(t 1) 6 t(...
 7.7.8.89: Model Railroads. An HO scale model railroad engine is 6 inches long...
 7.7.6.89: Solve each equation and check the result. If an equation has no sol...
 7.7.2.89: Perform the operations and simplify, if possible. 73p3 p 2p
 7.7.4.89: Perform the operations and simplify, if possible. 4b3 5b12
 7.7.1.89: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.3.89: Perform the operations. Then simplify, if possible. 5r 273r2 9r4r3r...
 7.7.5.89: What is a complex fraction? Give several examples.
 7.7.8.90: Model Railroads. An N scale model railroad caboose is 4.5 inches lo...
 7.7.6.90: Solve each equation and check the result. If an equation has no sol...
 7.7.2.90: Perform the operations and simplify, if possible. 5t211 2tt 5
 7.7.4.90: Perform the operations and simplify, if possible. 21y12 7y6
 7.7.1.90: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.3.90: Perform the operations. Then simplify, if possible. 9a5a2 25a a 505...
 7.7.5.90: Explain how to use method 1 to simplify: 1 1x3 1x
 7.7.8.91: Blueprints. The scale for the drawing shown means that a 14inch le...
 7.7.6.91: Solve each equation and check the result. If an equation has no sol...
 7.7.2.91: Perform the operations and simplify, if possible. 5x2 13x 6x 3 5x2 ...
 7.7.4.91: Perform the operations and simplify, if possible. a. 52x4x15b. 52x ...
 7.7.1.91: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.3.91: Perform the operations. Then simplify, if possible. 1136y936y
 7.7.5.91: Explain how to use method 2 to simplify the expression in 90.
 7.7.8.92: The Titanic. A 1:144 scale model of the Titanic is to be built. If ...
 7.7.6.92: Solve each equation and check the result. If an equation has no sol...
 7.7.2.92: Perform the operations and simplify, if possible. 3p2 5p 2p3 2p2 6p...
 7.7.4.92: Perform the operations and simplify, if possible. a. 2a 43 9a 25 b....
 7.7.1.92: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.3.92: Perform the operations. Then simplify, if possible. 1324w1724w
 7.7.5.92: a. List an advantage and a disadvantage of using method 1 to simpli...
 7.7.8.93: For each of the following purchases, determine the better buy. See ...
 7.7.6.93: Solve each equation and check the result. If an equation has no sol...
 7.7.2.93: Perform the operations and simplify, if possible. 4x2 12xy 9y2x3y2 ...
 7.7.4.93: Perform the operations and simplify, if possible. a. tt 5 tt2 25b. ...
 7.7.1.93: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.3.93: Perform the operations. Then simplify, if possible. 4x3x2 7x 2 3x 2...
 7.7.5.93: Simplify each expression. Write each answer without negative expone...
 7.7.8.94: For each of the following purchases, determine the better buy. See ...
 7.7.6.94: Solve each equation and check the result. If an equation has no sol...
 7.7.2.94: Perform the operations and simplify, if possible. ab425a2 16b2 25a2...
 7.7.4.94: Perform the operations and simplify, if possible. a. 1m 2 2m2 4m 4t...
 7.7.1.94: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.3.94: Perform the operations. Then simplify, if possible. 3c5c2 16c 3 2c ...
 7.7.5.94: Simplify each expression. Write each answer without negative expone...
 7.7.8.95: For each of the following purchases, determine the better buy. See ...
 7.7.6.95: For each expression, perform the indicated operations andthen simpl...
 7.7.2.95: Perform the operations and simplify, if possible. x 2x 2x2 xa
 7.7.4.95: Find the total height of the funnel.
 7.7.1.95: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.3.95: Perform the operations. Then simplify, if possible. 3x2x 1 x 2x 13c
 7.7.5.95: Simplify each expression. Write each answer without negative expone...
 7.7.8.96: For each of the following purchases, determine the better buy. See ...
 7.7.6.96: For each expression, perform the indicated operations andthen simpl...
 7.7.2.96: Perform the operations and simplify, if possible. y 3y 3y3 yx
 7.7.1.96: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.4.96: Funnels. Refer to the illustration on the right. What is the differ...
 7.7.3.96: Perform the operations. Then simplify, if possible. 8b23b 2 b2 43b 23x
 7.7.5.96: Simplify each expression. Write each answer without negative expone...
 7.7.8.97: For each of the following purchases, determine the better buy. See ...
 7.7.6.97: For each expression, perform the indicated operations and then simp...
 7.7.2.97: Perform the operations and simplify, if possible. a. 3x 64 4x 83y b...
 7.7.1.97: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.4.97: Explain the error: a. 11x yb. 3x x3 1 111 2
 7.7.3.97: Perform the operations. Then simplify, if possible. a. t125t12b. t1...
 7.7.5.97: Simplify. hh2 3h 24h 2 4h 1a
 7.7.8.98: For each of the following purchases, determine the better buy. See ...
 7.7.6.98: For each expression, perform the indicated operations andthen simpl...
 7.7.2.98: Perform the operations and simplify, if possible.a. 4a 85 5a 1043 b...
 7.7.1.98: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.4.98: Explain how to add two rational expressions with unlike denominators.
 7.7.3.98: Perform the operations. Then simplify, if possible. a. x92x9b. x9 2...
 7.7.5.98: Simplify. 2b2 1 3ab a3ab a 2b2 1
 7.7.5.99: Simplify. a a1 aa 12
 7.7.8.99: For each of the following purchases, determine the better buy. See ...
 7.7.6.99: Medicine. Radioactive tracers are used for diagnostic work in nucle...
 7.7.2.99: Perform the operations and simplify, if possible. a. x2 5x 62x 4 2x...
 7.7.1.99: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.4.99: When will the LCD of two rational expressions be the product of the...
 7.7.3.99: Perform the operations. Then simplify, if possible.a. m 65 m 25xb. ...
 7.7.5.100: Simplify. y2 1y2 1 a
 7.7.8.100: For each of the following purchases, determine the better buy. See ...
 7.7.6.100: Chemistry. Charless law describes the relationship between the volu...
 7.7.2.100: Perform the operations and simplify, if possible. a. x2 9x 209x 36 ...
 7.7.1.100: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.4.100: Explain how multiplication by 11 is used in this section.
 7.7.3.100: Perform the operations. Then simplify, if possible. a. 2r 92r 12r3 ...
 7.7.8.101: Height of a Tree. A tree casts a shadow of 26 feet at the same time...
 7.7.6.101: Electronics. Most electronic circuits require resistors to make the...
 7.7.2.101: Geometry. Find the area of the rectangle. 2x 14x2 7x 5 ft
 7.7.1.101: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.4.101: Find the slope and intercept of the graph of y 8x 2.
 7.7.3.101: Geometry. What is the difference of the length and width of the rec...
 7.7.8.102: Height of a Building. A man places a mirror on the ground and sees ...
 7.7.6.102: Mathematical Formulas. To quickly find the sum 12 14 18 116 132 164...
 7.7.2.102: Motion. The table contains algebraic expressions for the rate an ob...
 7.7.1.102: Simplify. If an expression cannot be simplified, write Does not sim...
 7.7.4.102: Find the slope and intercept of the graph of 3x 4y 36y.
 7.7.3.102: Geometry. What is the perimeter of the rectangle in 101?
 7.7.8.103: Surveying. To find the width of a river, a surveyor laid out the fo...
 7.7.6.103: Explain how the multiplication property of equality is used to solv...
 7.7.2.103: Talking. According to the Sacramento Bee newspaper, the number of w...
 7.7.1.103: Organ Pipes. The number of vibrations per second of an organ pipe i...
 7.7.4.103: What is the slope of the graph of y 2?
 7.7.3.103: Explain how to add fractions with the same denominator.
 7.7.6.104: When solving rational equations, how do you know whether a solution...
 7.7.8.104: Flight Paths. An airplane ascends 100 feet as it flies a horizontal...
 7.7.2.104: Classroom Space. The recommended size of an elementary school class...
 7.7.1.104: Raising Turkeys. The formula gives the number of turkeys on a poult...
 7.7.4.104: Is the graph of the equation x 0 the xaxis or the yaxis?
 7.7.3.104: Explain how to find a least common denominator.
 7.7.6.105: What is meant by clearing a rational equation of fractions? Give an...
 7.7.8.105: Slope. Find the unknown rise of the smaller slope triangle in the f...
 7.7.2.105: Natural Light. According to the University of Georgia School Design...
 7.7.1.105: Medical Dosages. The formula gives the concentration (in milligrams...
 7.7.4.105: Perform the operations and simplify the result, if possible. aa 1 2...
 7.7.3.105: Explain the error in the following solution: 2x 3x 5 x 2x 5 2x 3 x ...
 7.7.6.106: Explain the difference between the procedure used to simplify 1x 13...
 7.7.8.106: Washington, D.C. The Washington Monument casts a shadow of 166 12fe...
 7.7.2.106: Trucking. A cement truck holds 9 cubic yards of concrete. How many ...
 7.7.1.106: Manufacturing. If a company produces child car seats, the average c...
 7.7.4.106: Perform the operations and simplify the result, if possible. 2xx2 3...
 7.7.3.106: Explain the error in the following solution: y 4y 1y y 4 1y y 1 y 32y
 7.7.6.107: Uniforms. A cheerleading squad had their school mascot embroidered ...
 7.7.8.107: Explain how to solve the equation 76 2xand how to simplify the expr...
 7.7.2.107: Bears. The maximum speed a grizzly bear can run is about 30 miles p...
 7.7.1.107: Explain why x 77 x 1.
 7.7.4.107: Perform the operations and simplify the result, if possible. 1a 1 a...
 7.7.3.107: a. Explain why the LCD of 5h2and 3 2his h2 and not h3 . b. Explain ...
 7.7.6.108: Geometry. The vertex angle of an isosceles triangle is . Find the m...
 7.7.8.108: Explain why the concept of cross products cannot immediately be use...
 7.7.2.108: Fuel Economy. Use the information that follows to determine the mil...
 7.7.1.108: Explain why x 3x 4x is undefined for x 4 but defined for x 3.
 7.7.4.108: Perform the operations and simplify the result, if possible. 1 (x 2...
 7.7.3.108: Explain how multiplication by 1 is used to build a rational express...
 7.7.6.109: Solve each equation and check the result. If an equation has no sol...
 7.7.8.109: What are similar triangles?
 7.7.2.109: TV Trivia. On the comedy television series Green Acres (19651971), ...
 7.7.1.109: Explain the error in the following work: Simplify: xx 2 x1x1 2x
 7.7.3.109: Give the formula for . . . a. simple interestb. the area of a trian...
 7.7.6.110: Solve each equation and check the result. If an equation has no sol...
 7.7.8.110: What is a unit price? Give an example.
 7.7.2.110: Camping. The capacity of backpacks is usually given in cubic inches...
 7.7.1.110: Explain the error in the following work: Simplify: 30t 636 21 31 5 ...
 7.7.3.110: Give the formula for . . . a. the slope of a lineb. distance travel...
 7.7.6.111: Solve each equation and check the result. If an equation has no sol...
 7.7.8.111: Change 910to a percent.
 7.7.2.111: Explain how to multiply rational expressions.
 7.7.1.111: Explain why there are no values for for which x 7x2 49 xis undefined.
 7.7.3.111: Perform the operations. Simplify the result, if possible. 3xyx y x(...
 7.7.6.112: Engines. A formula that is used in the design and testing of diesel...
 7.7.8.112: Change 33 13%to a fraction.
 7.7.2.112: To divide rational expressions, you must first know how to multiply...
 7.7.1.112: Write a rational expression that is not defined for x 5. Then expla...
 7.7.3.112: Perform the operations. Simplify the result, if possible. 9t3 12t22...
 7.7.8.113: Find 30% of 1,600.
 7.7.2.113: Explain why 60 miles per hour and 1 mile per minute are the same sp...
 7.7.1.113: State each property using the variables a, b, and when necessary, c...
 7.7.3.113: Perform the operations. Simplify the result, if possible. 2a2 2a3 8...
 7.7.3.114: Perform the operations. Simplify the result, if possible. Find the ...
 7.7.8.114: Shopping. Maria bought a dress for 25% off the original price of $9...
 7.7.2.114: Explain why the unit conversion factor 1 ft12 in.is equal to 1.
 7.7.1.114: State each property using the variables a, b, and when necessary, c...
 7.7.8.115: Suppose ab cd. Write three other proportions using b, b, c, and d.
 7.7.2.115: Hardware. A brace has a length that is 2 inches less than twice the...
 7.7.1.115: Simplify. x2 2x 1)(x2 2x 1)(x2 1)2
 7.7.8.116: a. Verify that 35 1220 3 125 20. b. Is the following rule always tr...
 7.7.2.116: Solve A 1 2h(b d) for b.
 7.7.1.116: Simplify. 2x2 2x 12x3 3x2 4x 12(x
 7.7.2.117: Perform the operations. Simplify, if possible. c3 2c2 5c 10c2 c 2 c...
 7.7.1.117: Simplify. x3 27x3 9x2
 7.7.2.118: Perform the operations. Simplify, if possible. x3 y3x3 y3 x3 x2y xy...
 7.7.1.118: Simplify. b3 a3a2 ab b2x
 7.7.2.119: Perform the operations. Simplify, if possible. x3 x2 6x3x3 21x2 a2x...
 7.7.1.119: Simplify. m3 64m3 4m2 3m 12b3
 7.7.2.120: Perform the operations. Simplify, if possible. x2 y22x4 2x3 ax y2x2...
 7.7.1.120: Simplify. s3 s2 6s 6s3 1m3
Solutions for Chapter 7: Rational Expressions and Equations
Full solutions for Elementary and Intermediate Algebra  5th Edition
ISBN: 9781111567682
Solutions for Chapter 7: Rational Expressions and Equations
Get Full SolutionsSince 922 problems in chapter 7: Rational Expressions and Equations have been answered, more than 36297 students have viewed full stepbystep solutions from this chapter. Chapter 7: Rational Expressions and Equations includes 922 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Elementary and Intermediate Algebra was written by and is associated to the ISBN: 9781111567682. This textbook survival guide was created for the textbook: Elementary and Intermediate Algebra, edition: 5.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.