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: 8


$\displaystyle \frac{4}{x-2}, \qquad x\neq 2$

Work Step by Step

Numerator, factored:$\quad$ $4x-8=4(x-2)$ Denominator, factored: $x^{2}-4x+4=x^{2}-2\cdot x\cdot 2+2^{2}$=$\quad$... recognize a square of a difference $=(x-2)^{2}=(x-2)(x-2)$ Numbers to be excluded from the domain are numbers that yield 0 in the denominator: $x\neq 2$ Expression = $\displaystyle \frac{4(x-2)}{(x-2)(x-2)}$=$\qquad$... cancel $(x-2)$ = $\displaystyle \frac{4}{x-2}, \qquad x\neq 2$
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