Precalculus (6th Edition) Blitzer

Published by Pearson

Chapter P - Section P.6 - Rational Expressions - Exercise Set - Page 85: 37

Answer

$=3, \quad x\neq 2$

Work Step by Step

The fractions have a common denominator, we subtract the numerators... $\displaystyle \frac{4x-10}{x-2}-\frac{x-4}{x-2}=\frac{4x-10-(x-4)}{x-2}$ $=\displaystyle \frac{3x-6}{x-2}$ ... factor what we can... $=\displaystyle \frac{3(x-2)}{(x-2)}$ ... exclude values that yield 0 in the denominator: $x\neq 2$ ... and, cancel the common factor $=3, \quad x\neq 2$

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