Question

$\lim_{x \to \-1} (x^{2} +x ) / (x-1)$

Answer 1

The limit does not exist, since the limit from the left is $-\infty$ while the limit from the right is $+\infty$.

Or did you mean

$\displaystyle\lim_{x\to1}\frac{x^2-x}{x-1}\,?$

In that case, as $x\neq1$, we have

$\dfrac{x^2-x}{x-1}=\dfrac{x(x-1)}{x-1}=x$

which would make the limit 1.