Question

Calculate the following limits.
$\underset{x\to -3}{lim}\frac{x^2-9}{x^2+x-6}.$

Answer 1

$\underset{x\to -3}{lim}\frac{x^2-9}{x^2+x-6}$

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

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

$=\frac{6}{5}$