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: 57

Answer

$-\frac{x+9}{x+6}$

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: $\frac{x^{2}+7x-18}{-x^{2}-4x+12}$ =$\frac{x^{2}-2x+9x-18}{-x^{2}+2x-6x+12}$ =$\frac{x(x-2)+9(x-2))}{-x(x-2)-6(x-2)}$ =$\frac{(x-2)(x+9)}{(x-2)(-x-6)}$ =$\frac{(x+9)}{-x-6}$ =$\frac{x+9}{-(x+6)}$ =$-\frac{x+9}{x+6}$
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