## Problem Statement

Calculate the limit of the function:
$\lim _{x \rightarrow-1} \frac{x^{2}+3 x+2}{x^{3}+2 x^{2}-x-2}$
## Solution

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

## Problem Kuznetsov Limits 10-24