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: 64


$\displaystyle \frac{x-1}{x^{2}y},\qquad x\neq 0, y\neq 0$

Work Step by Step

Complex rational expressions have rational expressions in the numerator or/and in the denominator. Here, the numerator contains $\displaystyle \frac{1}{x}$ (exclusion from the domain: $x\neq 0.\ )$ To get rid of $\displaystyle \frac{1}{x}$, we multiply both the numerator and denominator with $x.$ $\displaystyle \frac{x}{x}\times\frac{1-\frac{1}{x}}{xy}=\frac{x-1}{x(xy)},\qquad x\neq 0, y\neq 0,x\neq-y$ The expression has no common factors. Nothing to reduce. $=\displaystyle \frac{x-1}{x^{2}y},\qquad x\neq 0, y\neq 0$
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