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

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