Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 7 - Algebraic Fractions - Chapter 7 Test - Page 323: 3

Answer

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

Work Step by Step

Since both the numerator and the denominator consist of trinomials, we can use the rules for factoring trinomials to factor these trinomails and cancel out the common factors: $\frac{2n^{2}-7n-4}{3n^{2}-8n-16}$ =$\frac{2n^{2}+1n-8n-4}{3n^{2}+4n-12n-16}$ =$\frac{n(2n+1)-4(2n+1)}{n(3n+4)-4(3n+4)}$ =$\frac{(2n+1)(n-4)}{(3n+4)(n-4)}$ =$\frac{(2n+1)}{(3n+4)}$
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