Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.2 - Multiplying and Dividing Rational Expressions - Exercise Set: 15

Answer

$\dfrac{x^{2}+6x+8}{x^{2}+x-20}\cdot\dfrac{x^{2}+2x-15}{x^2+8x+16}=\dfrac{(x+2)(x-3)}{(x-4)(x+4)}$

Work Step by Step

$\dfrac{x^{2}+6x+8}{x^{2}+x-20}\cdot\dfrac{x^{2}+2x-15}{x^2+8x+16}$ Factor both rational expressions completely: $\dfrac{x^{2}+6x+8}{x^{2}+x-20}\cdot\dfrac{x^{2}+2x-15}{x^2+8x+16}=\dfrac{(x+4)(x+2)}{(x+5)(x-4)}\cdot\dfrac{(x+5)(x-3)}{(x+4)^{2}}$ Multiply and then simplify by removing repeated factors in the numerator and the denominator: $...=\dfrac{(x+4)(x+2)(x+5)(x-3)}{(x+5)(x-4)(x+4)^{2}}=\dfrac{(x+2)(x-3)}{(x-4)(x+4)}$
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