The limit does not exist, since the limit from the left is [tex]-\infty[/tex] while the limit from the right is [tex]+\infty[/tex].
Or did you mean
[tex]\displaystyle\lim_{x\to1}\frac{x^2-x}{x-1}\,?[/tex]
In that case, as [tex]x\neq1[/tex], we have
[tex]\dfrac{x^2-x}{x-1}=\dfrac{x(x-1)}{x-1}=x[/tex]
which would make the limit 1.
