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: 34

Answer

$\frac{(3n+2)}{(n+4)}$

Work Step by Step

Since the numerator consists of a trinomial, we use the rules of factoring trinomials in order to factor it. For the case of the denominator, we use the rule $a^{2}-b^{2}=(a+b)(a-b)$ to factor it. Then, we cancel out the resultant common factors in the numerator and the denominator: $\frac{3n^{2}-10n-8}{n^{2}-16}$ =$\frac{3n^{2}+2n-12n-8}{n^{2}-4^{2}}$ =$\frac{n(3n+2)-4(3n+2)}{(n+4)(n-4)}$ =$\frac{(3n+2)(n-4)}{(n+4)(n-4)}$ =$\frac{(3n+2)}{(n+4)}$
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