## Calculus (3rd Edition)

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Since $x\rightarrow -\infty$, then $x$ is negative and hence we have $$\lim _{x \rightarrow-\infty} \frac{|x|+x}{x+1}=\lim _{x \rightarrow-\infty} \frac{-x+x}{x+1}=\lim _{x \rightarrow-\infty}0=0.$$