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: 13


$\displaystyle \frac{x+6}{x-6}, \qquad x\neq-6, 6$

Work Step by Step

Numerator, factored:$\quad$ $x^{2}+12x+36$=$x^{2}+2\cdot x\cdot 6+6^{2}$=$\quad$... recognize a square of a sum $=(x+6)^{2}=(x+6)(x+6)$ Denominator, factored: $x^{2}-36$=$\quad$... recognize a differrence of squares $=(x+6)(x-6)$ Numbers to be excluded from the domain are numbers that yield 0 in the denominator: $x\neq-6, 6$ Expression = $\displaystyle \frac{(x+6)(x+6)}{(x+6)(x-6)}$=$\qquad$... cancel $(x+6)$ = $\displaystyle \frac{x+6}{x-6}, \qquad x\neq-6, 6$
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