 82.1: 12 y 2 , 6 x
 82.2: 16a b 3, 5 b 2a 2 , 20ac
 82.3: x 2  2x, x 2  4
 82.4: x 3  4 x 2  5x, x 2 + 6x + 5
 82.5: 2 x 2 y  _x y
 82.6: 7a 15 b 2  _b 18ab
 82.7: 5 3m  _2 7m  _1 2m
 82.8: 3x 5  _1 2 x 2 + _3 4x
 82.9: 6 d 2 + 4d + 4 + _5 d + 2
 82.10: a a 2  a  20 + _2 a + 4
 82.11: 1 x 2  4 + _x x + 2
 82.12: x x + 1 + _3 x 2  4x  5
 82.13: x + _x _3 x  _x 6
 82.14: 1  _1 _x x  _1 x
 82.15: 2  _4 _x x  _4 x
 82.16: x  _x _2 x + _x 8
 82.17: GEOMETRY An expression for the area of a rectangle is 4x + 16. Find...
 82.18: 10 s 2 , 35 s 2 t 2
 82.19: 36 x2 y, 20xyz
 82.20: 4w  12, 2w  6 2
 82.21: x2  y 2 , x 3 + x 2 y
 82.22: 6 ab + _8 a
 82.23: 5 6v + _7 4v
 82.24: 3x 4 y 2  _ y 6x
 82.25: 5 a 2 b  _7a 5 a 2
 82.26: 7 y  8  _6 8  y
 82.27: a a  4  _3 4  a
 82.28: m m 2  4 + _2 3m + 6
 82.29: y y + 3  _ 6y y 2  9
 82.30: 5 x 2  3x  28 + _7 2x  14
 82.31: d  4 d 2 + 2d  8  _d + 2 d 2  16
 82.32: 1 b + 2 + _1 __b  5 2 b __ 2  b  3 b 2  3b  10
 82.33: (x + y)(_1 x  _1 __y) (x  y)(_1 x + _1 y)
 82.34: GEOMETRY An expression for the length of one rectangle is x _ 2  9...
 82.35: GEOMETRY Find the slope of a line that contains the points A (_1 p ...
 82.36: 14 a 3 , 15b c 3 , 12 b 3
 82.37: 9p2q3, 6pq4,4p3
 82.38: 2 t 2 + t  3, 2 t 2 + 5t + 3
 82.39: n 2  7n + 12, n 2  2n  8
 82.40: 5 r + 7 4
 82.41: _2x 3y + 5
 82.42: 3 4q  _2 5q  _1 2q
 82.43: 11 9  _7 2w  _6 5w
 82.44: 1 h 2  9h + 20  __5 h 2  10h + 25
 82.45: x x 2 + 5x + 6  _2 x 2 + 4x + 4
 82.46: m 2 + n _2 m 2  n 2 + _m n  m + _n m + n
 82.47: y + 1 y  1 + _ y + 2 y  2 + _ y y 2  3y + 2
 82.48: Write (_2s 2s + 1  1) (1 + _2s 1  2s) in simplest form.
 82.49: What is the simplest form of (3 + _5 a + 2) (3  _10 a + 7) ?
 82.50: GEOMETRY Find the perimeter of the quadrilateral. Express in simple...
 82.51: If R 1 is x ohms and R 2 is 4 ohms less than twice x ohms, write an...
 82.52: A circuit with two resistors connected in parallel has an effective...
 82.53: If x represents the faster pace in miles per hour, write an express...
 82.54: Write an expression for the time spent at the slower pace.
 82.55: Write an expression for the time Jalisa needed to complete the race.
 82.56: MAGNETS For a bar magnet, the magnetic field strength H at a point ...
 82.57: OPEN ENDED Write two polynomials that have a LCM of d 3  d.
 82.58: FIND THE ERROR Lorena and YongChan are simplifying _x a  _x b . W...
 82.59: CHALLENGE Find two rational expressions whose sum is __2x  1 (x + ...
 82.60: REASONING In the expression _1 a + _1 b + _1 c , a, b, and c are no...
 82.61: Writing in Math Use the information on page 450 to explain how subt...
 82.62: ACT/SAT What is the sum of _ x  y 5 and _ x + y 4 ? A _ x + 9y 20 ...
 82.63: REVIEW Given: Two angles are complementary. The measure of one angl...
 82.64: 9 x 2 y _ 3 (5xyz)2 (3xy) _ 3 20 x 2 y
 82.65: 5 a _ 2  20 2a + 2 _4a 10a  20
 82.66: Graph y x + 1 .
 82.67: g (x) = x 4  8 x 2  9
 82.68: h (x) = 3 x 3  5 x 2 + 13x  5
 82.69: GARDENS Helene Jonson has a rectangular garden 25 feet by 50 feet. ...
 82.70: Three times a number added to four times a second number is 22. The...
 82.71: x 2 + 3x + 2
 82.72: x 2  6x + 5
 82.73: x 2 + 11x  12
 82.74: x 2  16
 82.75: 3 x 2  75
 82.76: x 3  3 x 2 + 4x  12
Solutions for Chapter 82: Adding and Subtracting Rational Expressions
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 82: Adding and Subtracting Rational Expressions
Get Full SolutionsAlgebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302. Since 76 problems in chapter 82: Adding and Subtracting Rational Expressions have been answered, more than 61620 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 82: Adding and Subtracting Rational Expressions includes 76 full stepbystep solutions.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

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.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

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.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

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

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.