Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.6 - Rational Expressions - Exercise Set - Page 84: 12


$\displaystyle \frac{y-5}{y+4}, \qquad y\neq-4, -1$

Work Step by Step

Factoring $x^{2}+bx+c$, we search for two factors of c (m and n) such that m+n=b. If they exist, $x^{2}+bx+c =(x+m)(x+n)$ Numerator, factored:$\quad$ $y^{2}-4y-5$=$\quad$... we find factors $-5$ and $+1,$ $=(y-5)(y+1)$ Denominator, factored: $y^{2}+5y+4$=$\quad$... we find factors $+4$ and $+1.$ $=(y+4)(y+1)$ Numbers to be excluded from the domain are numbers that yield 0 in the denominator: $y\neq-4, -1$ Expression = $\displaystyle \frac{(y-5)(y+1)}{(y+4)(y+1)}$=$\qquad$... cancel $(y+1)$ = $\displaystyle \frac{y-5}{y+4}, \qquad y\neq-4, -1$
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