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: 36

Answer

$\frac{5x-2}{4x-3}$

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: $\frac{5x^{2}-32x+12}{4x^{2}-27x+18}$ =$\frac{5x^{2}-2x-30x+12}{4x^{2}-3x-24x+18}$ =$\frac{x(5x-2)-6(5x-2)}{x(4x-3)-6(4x-3)}$ =$\frac{(5x-2)(x-6)}{(4x-3)(x-6)}$ =$\frac{5x-2}{4x-3}$
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