## Problem Statement

Calculate the limit of the function:

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

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

## Problem Kuznetsov Limits 10-29