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: 52



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: $\frac{y^{2}+20y+96}{y^{2}+23y+120}$ =$\frac{y^{2}+8y+12y+96}{y^{2}+8y+15y+120}$ =$\frac{y(y+8)+12(y+8)}{y(y+8)+15(y+8)}$ =$\frac{(y+8)(y+12)}{(y+8)(y+15)}$ =$\frac{(y+12)}{(y+15)}$
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