Answer
Continuous at $ x=-1$
Work Step by Step
Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$.
$\lim_\limits{x \to -1^{-}} f(x)= \lim_\limits{x \to -1^{-}}\dfrac{x^2+x}{x^2-3x-4}=\dfrac{1}{5}$
and $\lim_\limits{x \to -1^{+}} f(x)= \lim_\limits{x \to -1^{+}}\dfrac{x}{x-4}=\dfrac{1}{5}$
So, $\lim_\limits{x \to -1^{-}} f(x)= \lim_\limits{x \to -1^{+}}f(x)$ exists.
Now, $\lim_\limits{x \to-1} f(x)=\dfrac{1}{5}$
and $ f(-1)=\dfrac{1}{5}$
so, $\lim_\limits{x \to 0} f(x) = f(0)$
Therefore, the function is continuous at $ x=-1$
