Answer
$2$
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.
$\lim_\limits{x\to 1} \dfrac{x^2+2x-13}{x^2-1}=\dfrac{\lim_\limits{x\to 1}
(x-1) (x+3)}{\lim_\limits{x\to 1} (x-1)(x+1)}=\lim_\limits{x\to 1} \dfrac{x+3}{x+1}=2$
