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: 60


$\displaystyle \frac{1}{4},\qquad x\neq 4$

Work Step by Step

Complex rational expressions have rational expressions in the numerator or/and in the denominator. Here, the numerator contains $\displaystyle \frac{x}{4}$. Multiplying with 4 would get rid of it. We also multiply the denominator with 4. $\displaystyle \frac{4}{4}\times\frac{\frac{x}{4}-1}{x-4}=\frac{x-4}{4(x-4)}$ The expression has a common factor. Reduce. $=\displaystyle \frac{1}{4},\qquad x\neq 4$ ($4$ is excluded as $(x-4)$; it was a part of the expression before reducing.)
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