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: 51

Answer

$\frac{(y-12)}{(y-14)}$

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: $\frac{y^{2}-6y-72}{y^{2}-8y-84}$ =$\frac{y^{2}+6y-12y-72}{y^{2}+6y-14y-84}$ =$\frac{y(y+6)-12(y+6)}{y(y+6)-14(y+6)}$ =$\frac{(y+6)(y-12)}{(y+6)(y-14)}$ =$\frac{(y-12)}{(y-14)}$
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