Answer
$0$
Work Step by Step
Since $ x\rightarrow -\infty $, then $ x $ is negative and hence we have
$$
\lim _{x \rightarrow-\infty} \frac{|x|+x}{x+1}=\lim _{x \rightarrow-\infty} \frac{-x+x}{x+1}=\lim _{x \rightarrow-\infty}0=0.
$$
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 - 2.7 Limits at Infinity - Exercises - Page 83: 29
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