## problem statement

Calculate the limit of the function:

$\lim _{x \rightarrow-1} \frac{\left(x^{3}-2 x-1\right)(x+1)}{x^{4}+4 x^{2}-5}$
## Solution

$$
\begin{aligned}
& \lim _{x \rightarrow-1} \frac{\left(x^{3}-2 x-1\right)(x+1)}{x^{4}+4 x^{2}-5}=\left\{\frac{0}{0}\right\}=\lim _{x \rightarrow-1} \frac{\left(x^{3}-2 x-1\right)(x+1)}{\left(x^{3}-x^{2}+5 x-5\right)(x+1)}= \\
& =\lim _{x \rightarrow-1} \frac{x^{3}-2 x-1}{x^{3}-x^{2}+5 x-5}=\frac{(-1)^{3}-2(-1)-1}{(-1)^{3}-(-1)^{2}+5(-1)-5}= \\
& =\frac{-1+2-1}{-1-1-5-5}=\frac{0}{-12}=0
\end{aligned}
$$

## Problem Kuznetsov Limits 10-1