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: 16


$=\displaystyle \frac{1}{2},\qquad x\displaystyle \neq 5,-\frac{3}{2}$

Work Step by Step

Factor what you can: $6x+9=3(2x+3)$ $3x-15=3(x-5)$ $x-5$ is factored $4x+6=2(2x+3)$ Expression $=\displaystyle \frac{3(2x+3)}{3(x-5)}\cdot\frac{(x-5)}{2(2x+3)}\qquad$ ...exclude the values that yield 0 in the denominator: $x\displaystyle \neq 5,-\frac{3}{2}$ ... cancel common factors: $3,\ (x-5)$, and $(2x+3)$ $=\displaystyle \frac{1}{2},\qquad x\displaystyle \neq 5,-\frac{3}{2}$
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