We have to find: lim x-->2 [(x^2-4)/(x^2+x-6)]

substituting x= 2 gives the indeterminate form 0/0. So we can substitute the numerator and the denominator with their derivatives using l'Hopital's rule.

=> lim x-->2 [ 2x / (2x + 1)]

Substitute x = 2

=> 4/ 5

**The required value of lim x-->2 [(x^2-4)/(x^2+x-6)] = 4/5**