Consider the complex fraction given in Exercise 1: 32 - 4316 - 512. Answereach part

Consider the complex fraction 3 2 - 4 3 1 6 - 5 12 . Answer each part, outlining Method 1 for simplifying this complex fraction. (a) To combine the terms in the numerator, we must find the LCD of and . What is this LCD? Determine the simplified form of the numerator of the complex fraction. (b) To combine the terms in the denominator, we must find the LCD of and . What is this LCD? Determine the simplified form of the denominator of the complex fraction. (c) Now use the results from parts (a) and (b) to write the complex fraction as a division problem using the symbol . (d) Perform the operation from part (c) to obtain the final simplification.

Consider the complex fraction given in Exercise 1: 3 2 - 4 3 1 6 - 5 12 . Answer each part, outlining Method 2 for simplifying this complex fraction. (a) We must determine the LCD of all the fractions within the complex fraction. What is this LCD? (b) Multiply every term in the complex fraction by the LCD found in part (a), but do not yet combine the terms in the numerator and the denominator. (c) Combine the terms from part (b) to obtain the simplified form of the complex fraction.

Which complex fraction is equivalent to 2 - 1 4 3 - 1 2 ? Answer this question without showing any work, and explain your reasoning. A. 2 + 1 4 3 + 1 2 B. 2 - 1 4 -3 + 1 2 C.-2 - 1 4 -3 - 1 2 D. -2 + 1 4 -3 + 1 2

Only one of these choices is equal to 1 3 + 1 12 1 2 + 1 4 . Which one is it? Answer this question without showing any work, and explain your reasoning. A. 5 9 B. 5 9 C. - 9 5 D. - 1 12

Simplify each complex fraction. Use either method. See Examples 16. - 4 3 2 9

Simplify each complex fraction. Use either method. See Examples 16. - 5 6 5 4

Simplify each complex fraction. Use either method. See Examples 16. x y2 x2 y

Simplify each complex fraction. Use either method. See Examples 16. p4 r p2 r2

Simplify each complex fraction. Use either method. See Examples 16. 4a4b3 3a 2ab4 b2

Simplify each complex fraction. Use either method. See Examples 16. 2r4t2 3t 5r2t5 3r

Simplify each complex fraction. Use either method. See Examples 16. m + 2 3 m - 4 m

Simplify each complex fraction. Use either method. See Examples 16. q - 5 q q + 5 3

Simplify each complex fraction. Use either method. See Examples 16. 2 x - 3 2 - 3x 2

Simplify each complex fraction. Use either method. See Examples 16. 6 + 2 r 3r + 1 4

Simplify each complex fraction. Use either method. See Examples 16. 1 x + x x2 + 1 8

Simplify each complex fraction. Use either method. See Examples 16. 3 m - m 3 - m2 4

Simplify each complex fraction. Use either method. See Examples 16. a - 5 a a + 1 a

Simplify each complex fraction. Use either method. See Examples 16. q + 1 q q + 4 q

Simplify each complex fraction. Use either method. See Examples 16. 5 8 + 2 3 7 3 - 1 4

Simplify each complex fraction. Use either method. See Examples 16. 6 5 - 1 9 2 5 + 5 3

Simplify each complex fraction. Use either method. See Examples 16. 1 x2 + 1 y2 1 x - 1 y

Simplify each complex fraction. Use either method. See Examples 16. 1 a2 - 1 b2 1 a - 1 b

Simplify each complex fraction. Use either method. See Examples 16. 2 p2 - 3 5p 4 p + 1 4p

Simplify each complex fraction. Use either method. See Examples 16. 2 m2 - 3 m 2 5m2 + 1 3m

Simplify each complex fraction. Use either method. See Examples 16. 5 x2y - 2 xy2 3 x2y2 + 4 xy

Simplify each complex fraction. Use either method. See Examples 16. 1 m3p + 2 mp2 4 mp + 1 m2p

Simplify each complex fraction. Use either method. See Examples 16. 1 4 - 1 a2 1 2 + 1 a

Simplify each complex fraction. Use either method. See Examples 16. 1 9 - 1 m2 1 3 + 1 m

Simplify each complex fraction. Use either method. See Examples 16. 1 z + 5 4 z2 - 25

Simplify each complex fraction. Use either method. See Examples 16. 1 a + 1 2 a2 - 1

Simplify each complex fraction. Use either method. See Examples 16. 1 m + 1 - 1 1 m + 1 + 1

Simplify each complex fraction. Use either method. See Examples 16. 2 x - 1 + 2 2 x - 1 - 2

Simplify each complex fraction. Use either method. See Examples 16. 1 m - 1 + 2 m + 2 2 m + 2 - 1 m - 3

Simplify each complex fraction. Use either method. See Examples 16. r + 3 - 1 r - 1 2 r + 2 + 3 r + 3

Simplify each complex fraction. Use either method. See Examples 16. 2 + 1 x - 28 x2 3 + 13 x + 4 x2

Simplify each complex fraction. Use either method. See Examples 16. 4 - 11 x - 3 x2 2 - 1 x - 15 x2

Simplify each complex fraction. Use either method. See Examples 16. y + 8 y - 4 y2 - 64 y2 - 16

Simplify each complex fraction. Use either method. See Examples 16. t + 5 t - 8 t2 - 25 t2 - 64

Simplify each fraction. 1 + x-1 - 12x-2 1 - x-1 - 20x-2

Simplify each fraction. 1 + t -1 - 56t -2 1 - t -1 - 72t -2

In a fraction, what operation does the fraction bar represent?

What property of real numbers justifies Method 2 of simplifying complex fractions?

To find the average of two numbers, we add them and divide by 2. Suppose that we wish to find the average of and . Work Exercises 43 46 in order, to see how a complex fraction occurs in a problem like this. Write in symbols: The sum of and , divided by 2. Your result should be a complex fraction.

To find the average of two numbers, we add them and divide by 2. Suppose that we wish to find the average of and . Work Exercises 43 46 in order, to see how a complex fraction occurs in a problem like this. Use Method 1 to simplify the complex fraction from Exercise 43.

To find the average of two numbers, we add them and divide by 2. Suppose that we wish to find the average of and . Work Exercises 43 46 in order, to see how a complex fraction occurs in a problem like this. Use Method 2 to simplify the complex fraction from Exercise 43.

To find the average of two numbers, we add them and divide by 2. Suppose that we wish to find the average of and . Work Exercises 43 46 in order, to see how a complex fraction occurs in a problem like this. Your answers in Exercises 44 and 45 should be the same. Which method did you prefer? Why?

The fractions in Exercises 4752 are called continued fractions. Simplify by starting at the bottom and working upward. 1 1 + 1 1 + 1 1

The fractions in Exercises 4752 are called continued fractions. Simplify by starting at the bottom and working upward. 5 5 + 5 5 + 5 5

The fractions in Exercises 4752 are called continued fractions. Simplify by starting at the bottom and working upward. 3 5 + 2 4 - 2 7

The fractions in Exercises 4752 are called continued fractions. Simplify by starting at the bottom and working upward. 2 4 + 2 4 - 2 3

The fractions in Exercises 4752 are called continued fractions. Simplify by starting at the bottom and working upward. r 4 - 2 6 + 2 r

The fractions in Exercises 4752 are called continued fractions. Simplify by starting at the bottom and working upward. q 6 + 8 4 + 4 2

Simplify. See Section 1.8. 9a b 4x 3 + 2 9 b

Simplify. See Section 1.8. 8a 3r 4 + 9 8 9a b

Simplify. See Section 1.8. -12a b 11p2 3 - 9p 4 b

Simplify. See Section 1.8. 6a 5z2 2 - 8z 3 -12a b

Solve each equation. See Sections 2.3 and 6.5. 3x + 5 = 7x + 3

Solve each equation. See Sections 2.3 and 6.5. 9z + 2 = 7z + 6

Solve each equation. See Sections 2.3 and 6.5. 61z - 32 + 5 = 8z - 3

Solve each equation. See Sections 2.3 and 6.5. k2+ 3k - 4 = 0