The function f(x) = [x^2 + x] / [x] is defined and continuous for all x except x = 0. What value of x must be assigned to f(x) for x = 0 in order that the function be continuous at x = 0?

In order for $f$ to be continuous at $0$, the definition of continuous says we must have:
${\lim}_{x \rightarrow 0} f \left(x\right) = f \left(0\right)$
This question asks what number must you put on the right (as $f \left(0\right)$) in order for the equation to be true.
${\lim}_{x \rightarrow 0} \frac{{x}^{2} + x}{x}$