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 85: 49


$\displaystyle \frac{13}{6(x+2)},\quad x\neq-2$

Work Step by Step

Factor each denominator. $\displaystyle \frac{3}{2x+4}+\frac{2}{3x+6}=\frac{3}{2(x+2)}+\frac{2}{3(x+2)}$ The denominators are different. Find a common denominator. LCD=$2(x+2)\cdot 3=6(x+2)$ $=\displaystyle \frac{3}{2(x+2)}\times\frac{3}{3}+\frac{2}{3(x+2)}\times\frac{2}{2}$ $=\displaystyle \frac{9}{6(x+2)}+\frac{4}{6(x+2)}$ $=\displaystyle \frac{9+4}{6(x+2)}$ =$\displaystyle \frac{13}{6(x+2)},\quad x\neq-2$
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