Question

Evaluate the following limit.

${\displaystyle \underset{x->2}{lim}\frac{3x^2-x-10}{x^2-4}}$

Answer 1

${\displaystyle \underset{x\to 2}{lim}\frac{3x^2-x-10}{x^2-4}}$

= ${\displaystyle \underset{x\to 2}{lim}\frac{(x-2)(3x+5)}{(x-2)(x+2)}}$

= ${\displaystyle \underset{x\to 2}{lim}\frac{(3x+5)}{(x+2)}}$

= ${\displaystyle \frac{3\times 2+5}{2+2}}$

= ${\displaystyle \frac{11}{4}}$