Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Review: 19

Answer

$\dfrac{x^{2}-5x-24}{x^{2}-x-12}\div\dfrac{x^{2}-10x+16}{x^{2}+x-6}=\dfrac{x+3}{x-4}$

Work Step by Step

$\dfrac{x^{2}-5x-24}{x^{2}-x-12}\div\dfrac{x^{2}-10x+16}{x^{2}+x-6}$ Factor both rational expressions completely: $\dfrac{(x-8)(x+3)}{(x-4)(x+3)}\div\dfrac{(x-8)(x-2)}{(x+3)(x-2)}=...$ Evaluate the division and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression: $...=\dfrac{(x-8)(x+3)^{2}(x-2)}{(x-4)(x+3)(x-8)(x-2)}=\dfrac{x+3}{x-4}$
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