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: 55

Answer

$\frac{(x+2)}{(5x+4)}$

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: $\frac{-2x^{2}-x+6}{-10x^{2}+7x+12}$ =$\frac{-(2x^{2}+x-6)}{-(10x^{2}-7x-12)}$ =$\frac{-(2x^{2}-3x+4x-6)}{-(10x^{2}+8x-15x-12)}$ =$\frac{-(x(2x-3)+2(2x-3))}{-(2x(5x+4)-3(5x+4))}$ =$\frac{-(2x-3)(x+2)}{-(5x+4)(2x-3)}$ =$\frac{-(x+2)}{-(5x+4)}$ =$\frac{(x+2)}{(5x+4)}$
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