`lim_(x->1) (x^2 - 1)/(x^2 - x)` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t...

`lim_(x->1) (x^2 - 1)/(x^2 - x)` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why.

Expert Answers
gsarora17 eNotes educator| Certified Educator

`lim_(x->1)(x^2-1)/(x^2-x)`

`=lim_(x->1)((x+1)(x-1))/(x(x-1))`

`=lim_(x->1)(x+1)/x`

plug in the value,

`=(1+1)/1`

=2