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: 40


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

Work Step by Step

The fractions have a common denominator, we subtract the numerators... $\displaystyle \frac{x^{2}-4x}{x^{2}-x-6}-\frac{x-6}{x^{2}-x-6}=\frac{x^{2}-4x-(x-6)}{x^{2}-x-6}$ $=\displaystyle \frac{x^{2}-5x+6}{x^{2}-x-6}$ ... factor what we can; for trinomials $x^{2}+bx+c,$ we search for two factors of c whose sum is b $=\displaystyle \frac{(x-2)(x-3)}{(x-3)(x+2)}$ ... exclude values that yield 0 in the denominator: $x\neq-2,3$ ... and, cancel the common factor $=\displaystyle \frac{x-2}{x+2}, \quad x\neq-2,3$
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