Answer
$5$
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.
$\lim_\limits{x\to 3} \dfrac{x^2-4}{x-2}=\dfrac{\lim_\limits{x\to 3}
(x-2)(x+2)}{\lim_\limits{x\to 3} x-2}=\lim_\limits{x\to 3} x-2=5$
