Evaluate

To evaluate:

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

Formula used:

We have,

$\lim _{x \rightarrow a} f(x)=f(a)$ and

As $\mathrm{X} \rightarrow 3$, we have

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

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

$\lim _{x \rightarrow 3} \frac{x^{2}-4 x+3}{x^{2}-2 x-3}=\frac{2}{5}$

Thus, the value of

$\lim _{x \rightarrow 3} \frac{x^{2}-4 x+3}{x^{2}-2 x-3}$ is $\frac{2}{5}$