Evaluate the limit of the fraction (x^2-4)/(x^2+x-6) as x approaches to 2.

First, we'll substitute x by 2 and we'll verify if it is
an indetermination:

lim (x^2-4)/(x^2+x-6) =
(2^2-4)/(2^2+2-6) = (4-4)/(4+2-6) = 0/0

Since we've get an
indetermination, "0/0" type, we'll apply L'Hospital
rule:

lim (x^2-4)/(x^2+x-6) = lim
(x^2-4)'/(x^2+x-6)'

lim (x^2-4)'/(x^2+x-6)' = lim
2x/(2x+1)

We'll substitute again x by
2:

 lim 2x/(2x+1) = 2*2/(2*2+1) =
4/5

The limit of the fraction, as x
approaches to 2, is: lim (x^2-4)/(x^2+x-6) = 4/5.