Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 7 - Algebraic Fractions - 7.1 - Simplifying Algebraic Fractions - Problem Set 7.1: 26

Answer

$\frac{5x}{x-5}$

Work Step by Step

To factor the denominator, we use the rule $a^{2}-b^{2}=(a+b)(a-b)$. Then, we factor the expression in the numerator in order to cancel out common factors in the numerator and the denominator: $\frac{5x^{2}+25x}{x^{2}-25}$ =$\frac{5x(x+5)}{x^{2}-5^{2}}$ =$\frac{5x(x+5)}{(x+5)(x-5)}$ =$\frac{5x}{x-5}$
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