find the limit as x --> -2 (x^3+8) / (x^2-4)?

Question

how do you factor the top so i can cross something out with the (x+2)(x-2) on the bottom?

Answer 1

x^3+8/x^2-4
=(x+2)(x^2-x+4)/(x+2)(x-2)
=(x^2-2x+4)/(x-2)
applyingthelimits
=4+4+4/-2-2
=-3

Answer 2

use L'Hopital's rule, and take the derivative of both the top and bottom. then you get lim (as x->-2) of 3x^2 / 2x
plug in -2, and it's 3*(-2)^2 / 2*-2, which is 24 / -4, or

-6

Answer 3

Factor out (x+2) top and bottom. It will look muuuuch nicer.