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 - Page 281: 47



Work Step by Step

We factor the expression in the denominator by taking out $8$ as the common factor. Since the numerator consists of a trinomial, we use the rules of factoring trinomials in order to factor it. Then, we cancel out the resultant common factors in the numerator and the denominator: $\frac{n^{2}+14n+49}{8n+56}$ =$\frac{n^{2}+7n+7n+49}{8(n+7)}$ =$\frac{n(n+7)+7(n+7)}{8(n+7)}$ =$\frac{(n+7)(n+7)}{8(n+7)}$ =$\frac{(n+7)}{8}$
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