Answer
The limit does not exist. It approaches $-\infty $ as $ x $ approaches $-1^+$.
Work Step by Step
By substituting, we have
$$
\lim _{x \rightarrow -1^+} \frac{1}{x+1}=\frac{1}{-1+1}=\frac{1}{0}
.
$$ So the limit does not exist. It approaches $\infty $ as $ x $ approaches $-1^+$. Graphing confirms that the one-sided limits are infinite.
