Question

Calculate the following limits.
$\underset{x\to 3}{lim}\frac{x^2-5x+6}{x-3}.$

Answer 1

$\underset{x\to 3}{lim}\frac{x^2-5x+6}{x-3}$

$=\underset{x\to 3}{lim}\frac{(x-2)(x-3)}{x-3}$

$=\underset{x\to 3}{lim}(x-2)=3-2$

$=1$