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: 50

Answer

$\frac{(3n+5)}{(n-2)}$

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: $\frac{9n^{2}+30n+25}{3n^{2}-n-10}$ =$\frac{9n^{2}+15n+15n+25}{3n^{2}+5n-6n-10}$ =$\frac{3n(3n+5)+5(3n+5)}{n(3n+5)-2(3n+5)}$ =$\frac{(3n+5)(3n+5)}{(3n+5)(n-2)}$ =$\frac{(3n+5)}{(n-2)}$
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