Answer
Since $~~\lim\limits_{x \to 1}f(x) \neq f(1)$, the function is not continuous at $x = 1$
Work Step by Step
$f(1) = 1$
We can find the limit of the function at $x=1$:
$\lim\limits_{x \to 1}f(x) = \frac{x^2-x}{x^2-1}$
$\lim\limits_{x \to 1}f(x) = \frac{x(x-1)}{(x-1)(x+1)}$
$\lim\limits_{x \to 1}f(x) = \frac{x}{x+1}$
$\lim\limits_{x \to 1}f(x) = \frac{1}{2}$
Since $~~\lim\limits_{x \to 1}f(x) \neq f(1)$, the function is not continuous at $x = 1$
