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: 38


$=\displaystyle \frac{x}{x-2}, \quad x\neq 2$

Work Step by Step

The fractions have a common denominator, we subtract the numerators... $\displaystyle \frac{2x+3}{3x-6}-\frac{3-x}{3x-6}=\frac{2x+3-(3-x)}{3x-6}$ $=\displaystyle \frac{3x}{3x-6}$ ... factor what we can... $=\displaystyle \frac{3x}{3(x-2)}$ ... exclude values that yield 0 in the denominator: $x\neq 2$ ... and, cancel the common factor $=\displaystyle \frac{x}{x-2}, \quad x\neq 2$
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