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: 42

Answer

$\frac{(3a+2)}{(4a-1)}$

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: $\frac{6a^{2}-11a-10}{8a^{2}-22a+5}$ =$\frac{6a^{2}+4a-15a-10}{8a^{2}-2a-20a+5}$ =$\frac{2a(3a+2)-5(3a+2)}{2a(4a-1)-5(4a-1)}$ =$\frac{(3a+2)(2a-5)}{(4a-1)(2a-5)}$ =$\frac{(3a+2)}{(4a-1)}$
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