Answer
$\dfrac{6}{7}$
Work Step by Step
Recall the limit rules:
$ \ Rule -\ 1 \ : \lim\limits_{x \to a} [A(x)]^n =[\lim\limits_{x \to a} A(x)]^n $
$\ Rule \ - \ 2 : \lim\limits_{x \to a} A(x)=A(a)$
$\ Rule \ - \ 3: \lim\limits_{x \to a} \dfrac{A(x)}{B(x)}=\dfrac{\lim\limits_{x \to a} A(x)}{\lim\limits_{x \to a} B(x)}$
$\lim_{x\to -3}\dfrac{x^2-9}{x^2-x-12}\\=\lim_{x\to -3} \dfrac{(x+3)(x-3)}{(x+3)(x-4)}$
Apply $\lim\limits_{x \to a} \dfrac{A(x)}{B(x)}=\dfrac{\lim\limits_{x \to a} A(x)}{\lim\limits_{x \to a} B(x)}$
$\lim_{x\to -3}\dfrac{x-3}{x-4}=\dfrac{-3-3}{-3-7} \\=\dfrac{6}{7}$
