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: 48

Answer

$\frac{6}{(n-10)}$

Work Step by Step

We factor the expression in the numerator by taking out $6$ as the common factor. Since the denominator 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: $\frac{6n-60}{n^{2}-20n+100}$ =$\frac{6(n-10)}{n^{2}-10n-10n+100}$ =$\frac{6(n-10)}{n(n-10)-10(n-10)}$ =$\frac{6(n-10)}{(n-10)(n-10)}$ =$\frac{6}{(n-10)}$
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