Answer
$\dfrac{5}{6}$
Work Step by Step
Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$.
In order to to find the limit, we will plug $ a $ into the function and then simplify.
$\lim_\limits{x\to 3} \dfrac{x^2-x-6}{x^2-9}=\dfrac{\lim_\limits{x\to 3}
(x+2) (x-3)}{\lim_\limits{x\to 3} (x-3)(x+3)}=\lim_\limits{x\to 3} \dfrac{x+2}{x+3}=\dfrac{5}{6}$
