Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Review: 66

Answer

$\dfrac{x^{2}-x-72}{x^{2}-x-30}\div\dfrac{x^{2}+6x-27}{x^{2}-9x+18}=\dfrac{(x-9)(x+8)}{(x+5)(x+9)}$

Work Step by Step

$\dfrac{x^{2}-x-72}{x^{2}-x-30}\div\dfrac{x^{2}+6x-27}{x^{2}-9x+18}$ Factor both rational expressions completely: $\dfrac{(x-9)(x+8)}{(x-6)(x+5)}\div\dfrac{(x+9)(x-3)}{(x-6)(x-3)}=...$ Evaluate the division and simplify by removing the factors that appear both in the numerator and the denominator: $...=\dfrac{(x-9)(x+8)(x-6)(x-3)}{(x-6)(x+5)(x+9)(x-3)}=\dfrac{(x-9)(x+8)}{(x+5)(x+9)}$
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