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: 31

Answer

$\frac{n}{(n+1)}$

Work Step by Step

We factor the expression in the numerator by taking out $n$ 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: $\frac{n^{2}+2n}{n^{2}+3n+2}$ =$\frac{n(n+2)}{n^{2}+1n+2n+2}$ =$\frac{n(n+2)}{n(n+1)+2(n+1)}$ =$\frac{n(n+2)}{(n+1)(n+2)}$ =$\frac{n}{(n+1)}$
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