Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Review: 65

Answer

$\dfrac{x^{2}+9x+20}{x^{2}-25}\cdot\dfrac{x^{2}-9x+20}{x^{2}+8x+16}=\dfrac{x-4}{x+4}$

Work Step by Step

$\dfrac{x^{2}+9x+20}{x^{2}-25}\cdot\dfrac{x^{2}-9x+20}{x^{2}+8x+16}$ Factor both rational expressions completely: $\dfrac{(x+5)(x+4)}{(x-5)(x+5)}\cdot\dfrac{(x-5)(x-4)}{(x+4)^{2}}=...$ Evaluate the product and simplify by removing the factors that appear both in the numerator and the denominator: $...=\dfrac{(x+5)(x+4)(x-5)(x-4)}{(x-5)(x+5)(x+4)^{2}}=\dfrac{x-4}{x+4}$
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