Question

Evaluate the Given limit: $\underset{x\to 2}{lim}\frac{3x^2-x-10}{x^2-4}$

Answer 1

$\underset{x\to 2}{lim}\frac{3x^2-x-10}{x^2-4}=\underset{x\to 2}{lim}\frac{(x-2)(3x+5)}{(x-2)(x+2)}$
$=\underset{x\to 2}{lim}\frac{3x+5}{x+2}=\frac{3\left(2\right)+5}{2+2}=\frac{11}{4}$