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