College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.6 - Page 86: 13


$\frac{x+6}{x-6}$; $x \ne -6, 6$

Work Step by Step

To begin with, we will need to factor the numerator and the denominator. The numerator is a perfect square trinomial and the denominator is a difference of squares. $\frac{(x+6)(x+6)}{(x+6)(x-6)}$ Here, we can see that the $x + 6$ factors cancel out. As a result, we are left with $\frac{x+6}{x-6}$. This still will only hold true as long as we include our domain restrictions from earlier. This means that we must set the original denominator equal to 0: $(x+6)(x - 6) = 0$ This means that $x = 6$ and $x = -6$ are both domain restrictions.
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