## Problem Statement

Calculate the limit of the function:

$\lim _{x \rightarrow-1} \frac{x^{3}-2 x-1}{x^{4}+2 x+1}$
## Solution

$$
\begin{aligned}
& \lim _{x \rightarrow-1} \frac{x^{3}-2 x-1}{x^{4}+2 x+1}=\left\{\frac{0}{0}\right\}=\lim _{x \rightarrow-1} \frac{(x+1)\left(x^{2}-x-1\right)}{(x+1)\left(x^{3}-x^{2}+x+1\right)}= \\
& =\lim _{x \rightarrow-1} \frac{x^{2}-x-1}{x^{3}-x^{2}+x+1}=\frac{(-1)^{2}-(-1)-1}{(-1)^{3}-(-1)^{2}+(-1)+1}= \\
& =\frac{1+1-1}{-1-1-1+1}=\frac{1}{-2}=-\frac{1}{2}
\end{aligned}
$$

## Problem Kuznetsov Limits 10-27