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: 40

Answer

$\frac{x-6}{x+4}$

Work Step by Step

Since the numerator and the denominator both consist of a trinomial, we use the rules of factoring trinomials in order to factor them. Then, we cancel out the resultant common factors in the numerator and the denominator: $\frac{8x^{2}-51x+18}{8x^{2}+29x-12}$ =$\frac{8x^{2}-3x-48x+18}{8x^{2}-3x+32x-12}$ =$\frac{x(8x-3)-6(8x-3)}{x(8x-3)+4(8x-3)}$ =$\frac{(8x-3)(x-6)}{(8x-3)(x+4)}$ =$\frac{x-6}{x+4}$
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