College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.2 - Algebra Essentials - R.2 Assess Your Understanding - Page 27: 61

Answer

$(a)$

Work Step by Step

RECALL: The denominator of a rational expression is not allowed to be equal to zero since division of zero is undefined. Factor the denominator using the formula $a^2-b^2=(a-b)(a+b)$ to obtain: $\dfrac{x}{x^2-9} = \dfrac{x}{x^2-3^2}=\dfrac{x}{(x-3)(x+3)}$ Find the values of $x$ that will make the denominator equal to zero by using the zero-factor theorem. Equate each factor of the denominator to zero, and then solve each equation to obtain: $\begin{array}{ccc} \\&x-3 = 0 &\text{ or } &x + 3 = 0 \\&x = 3 &\text{ or } &x=-3 \\\end{array}$ Thus, in the given expression, $x$ cannot be equal to $-3$ or $3$ since they make the denominator equal to 0. Therefore, the answer is $(a)$.
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