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 - Page 281: 25



Work Step by Step

To factor the numerator, we use the rule $a^{2}-b^{2}=(a+b)(a-b)$. Then, we factor the expression in the denominator in order to cancel out common factors in the numerator and the denominator: $\frac{x^{2}-1}{3x^{2}-3x}$ =$\frac{x^{2}-1^{2}}{3x(x-1)}$ =$\frac{(x+1)(x-1)}{3x(x-1)}$ =$\frac{(x+1)}{3x}$
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