Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Review: 17

Answer

$\dfrac{x^{2}-9}{x^{2}-4}\cdot\dfrac{x-2}{x+3}=\dfrac{x-3}{x+2}$

Work Step by Step

$\dfrac{x^{2}-9}{x^{2}-4}\cdot\dfrac{x-2}{x+3}$ Factor the first rational expression completely: $\dfrac{x^{2}-9}{x^{2}-4}\cdot\dfrac{x-2}{x+3}=\dfrac{(x-3)(x+3)}{(x-2)(x+2)}\cdot\dfrac{x-2}{x+3}=...$ Evaluate the product and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression: $...=\dfrac{(x-3)(x+3)(x-2)}{(x-2)(x+2)(x+3)}=\dfrac{x-3}{x+2}$
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