`lim_(x->2) (x^2 + x - 6)/(x - 2)` 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->2) (x^2 + x - 6)/(x - 2)` 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->2)(x^2+x-6)/(x-2)`

`=lim_(x->2)((x-2)(x+3))/(x-2)`

`=lim_(x->2)(x+3)`

plug in the value,

=(2+3)

=5