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: 41

Answer

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

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: $\frac{10a^{2}+a-3}{15a^{2}+4a-3}$ =$\frac{10a^{2}-5a+6a-3}{15a^{2}-5a+9a-3}$ =$\frac{5a(2a-1)+3(2a-1)}{5a(3a-1)+3(3a-1)}$ =$\frac{(2a-1)(5a+3)}{(3a-1)(5a+3)}$ =$\frac{(2a-1)}{(3a-1)}$
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