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: 35


$=\displaystyle \frac{2x-1}{x+3}, \quad x\neq 0,-3$

Work Step by Step

The fractions have a common denominator, we add the numerators... $\displaystyle \frac{x^{2}-2x}{x^{2}+3x}+\frac{x^{2}+x}{x^{2}+3x}=\frac{x^{2}-2x+x^{2}+x}{x^{2}+3x}$ $=\displaystyle \frac{2x^{2}-x}{x^{2}+3x}$ ... factor what we can... $=\displaystyle \frac{x(2x-1)}{x(x+3)}$ ... exclude values that yield 0 in the denominator: $x\neq 0,-3$ ... and, cancel the common factor $=\displaystyle \frac{2x-1}{x+3}, \quad x\neq 0,-3$
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