 R.7 .1: When the numerator and denominator of a rational expression contain...
 R.7 .2: LCM is an abbreviation for .
 R.7 .3: True or False The rational expression is reduced to lowest terms.
 R.7 .4: True or False The LCM of and is 4x3 (x + 1).
 R.7 .5: In 516, reduce each rational expression to lowest terms. 3x + 9 x2  9
 R.7 .6: In 516, reduce each rational expression to lowest terms. 4x2 + 8x 1...
 R.7 .7: In 516, reduce each rational expression to lowest terms. x2  2x 3x...
 R.7 .8: In 516, reduce each rational expression to lowest terms. 15x2 + 24x...
 R.7 .9: In 516, reduce each rational expression to lowest terms. 24x2 12x2 ...
 R.7 .10: In 516, reduce each rational expression to lowest terms. x2 + 4x + ...
 R.7 .11: In 516, reduce each rational expression to lowest terms. y2  25 2y...
 R.7 .12: In 516, reduce each rational expression to lowest terms. 3y2  y  ...
 R.7 .13: In 516, reduce each rational expression to lowest terms. x2 + 4x  ...
 R.7 .14: In 516, reduce each rational expression to lowest terms. x  x2 x2 ...
 R.7 .15: In 516, reduce each rational expression to lowest terms. x2 + 5x  ...
 R.7 .16: In 516, reduce each rational expression to lowest terms. 2x2 + 5x ...
 R.7 .17: In 1734, perform the indicated operation and simplify the result. L...
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 R.7 .53: In 5360, find the LCM of the given polynomials x2  4, x2  x  2
 R.7 .54: In 5360, find the LCM of the given polynomials x2  x  12, x2  8x...
 R.7 .55: In 5360, find the LCM of the given polynomials x3  x, x2  x
 R.7 .56: In 5360, find the LCM of the given polynomials 3x2  27, 2x2  x  15
 R.7 .57: In 5360, find the LCM of the given polynomials 4x3  4x2 + x, 2x3 ...
 R.7 .58: In 5360, find the LCM of the given polynomials x  3, x2 + 3x, x3  9x
 R.7 .59: In 5360, find the LCM of the given polynomials x3  x, x3  2x2 + x...
 R.7 .60: In 5360, find the LCM of the given polynomials x2 + 4x + 4, x3 + 2x...
 R.7 .61: In 6172, perform the indicated operations and simplify the result. ...
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 R.7 .85: In 8592, expressions that occur in calculus are given. Reduce each ...
 R.7 .86: In 8592, expressions that occur in calculus are given. Reduce each ...
 R.7 .87: In 8592, expressions that occur in calculus are given. Reduce each ...
 R.7 .88: In 8592, expressions that occur in calculus are given. Reduce each ...
 R.7 .89: In 8592, expressions that occur in calculus are given. Reduce each ...
 R.7 .90: In 8592, expressions that occur in calculus are given. Reduce each ...
 R.7 .91: In 8592, expressions that occur in calculus are given. Reduce each ...
 R.7 .92: In 8592, expressions that occur in calculus are given. Reduce each ...
 R.7 .93: The Lensmakers Equation The focal length of a lens with index of re...
 R.7 .94: Electrical Circuits An electrical circuit contains three resistors ...
 R.7 .95: The following expressions are called continued fractions: Each simp...
 R.7 .96: Explain to a fellow student when you would use the LCM method to ad...
 R.7 .97: Which of the two methods given in the text for simplifying complex ...
Solutions for Chapter R.7 : Rational Expressions
Full solutions for College Algebra  9th Edition
ISBN: 9780321716811
Solutions for Chapter R.7 : Rational Expressions
Get Full SolutionsSince 97 problems in chapter R.7 : Rational Expressions have been answered, more than 33989 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: College Algebra, edition: 9. College Algebra was written by and is associated to the ISBN: 9780321716811. Chapter R.7 : Rational Expressions includes 97 full stepbystep solutions.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

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

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.

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.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

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.

Iterative method.
A sequence of steps intended to approach the desired solution.

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

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

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

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).