## Problem Statement

Calculate the limit of the function:

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

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

$=\lim _{x \rightarrow 1}\left(\frac{x+3}{x+5}\right)^{\frac{1}{2-x}}=\left(\frac{1+3}{1+5}\right)^{\frac{1}{2-1}}=\left(\frac{4}{6}\right)^{1}=\frac{2}{3}$

## Problem Kuznetsov Limits 20-29