Answer
$\frac{5}{3}.$
Work Step by Step
We have $$
\lim _{x \rightarrow 2} \frac{x^{2}+x-6}{x^{2}-x-2}=
\lim _{x \rightarrow 2} \frac{(x+3)(x-2)}{(x-2)(x+1)}=\lim _{x \rightarrow 2} \frac{x+3}{x+1}=\frac{5}{3}.
$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 2 - Limits - 2.2 Limits: A Numerical and Graphical Approach - Exercises - Page 54: 19
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