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