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: 13

Answer

$\dfrac{x^{2}-25}{x^{2}-3x-10}\cdot\dfrac{x+2}{x}=\dfrac{x+5}{x}$

Work Step by Step

$\dfrac{x^{2}-25}{x^{2}-3x-10}\cdot\dfrac{x+2}{x}$ Factor the numerator and the denominator of the first fraction: $\dfrac{x^{2}-25}{x^{2}-3x-10}\cdot\dfrac{x+2}{x}=\dfrac{(x-5)(x+5)}{(x+2)(x-5)}\cdot\dfrac{x+2}{x}=...$ Multiply both rational expressions and simplify by removing repeated factors in the numerator and the denominator: $...=\dfrac{(x-5)(x+5)(x+2)}{x(x+2)(x-5)}=\dfrac{x+5}{x}$
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