Answer
does not exist.
Work Step by Step
See table below.
As x approaches the value $-1$ from the left,
$f(x)$ seems to approach the value $-200,000$
As x approaches the value $-1$ from the right,
$f(x)$ seems to approach the value $+200,000$
If $f(x)$ fails to approach a single fixed number as $x$ approaches $a$ from both sides, then we say that $f(x)$ has no limit as $x\rightarrow a$, or $\displaystyle \lim_{x\rightarrow a}f(x)$ does not exist.
Thus, $\displaystyle \lim_{x\rightarrow-1} \frac{x^{2}1}{x+1}$ does not exist.
