Condition of the problem

Calculate the limit of the function:

$$
\lim _{x \rightarrow-1} \frac{x^{3}-3 x-2}{x^{2}+2 x+1}
$$
## Solution

$$
\begin{aligned}
& \lim _{x \rightarrow-1} \frac{x^{3}-3 x-2}{x^{2}+2 x+1}=\left\{\frac{0}{0}\right\}=\lim _{x \rightarrow-1} \frac{(x+1)\left(x^{2}-x-2\right)}{(x+1)^{2}}= \\
& =\lim _{x \rightarrow-1} \frac{x^{2}-x-2}{x+1}=\left\{\frac{0}{0}\right\}=\lim _{x \rightarrow-1} \frac{(x+1)(x-2)}{x+1}= \\
& =\lim _{x \rightarrow-1}(x-2)=-1-2=-3
\end{aligned}
$$

## Problem Kuznetsov Limits 10-21