Given fx x2 7x 12x2 2x 24 Find any vertical asymptotes

Given f(x) = x^2 + 7x + 12/x^2 - 2x - 24 Find: any vertical asymptotes. any holes. horizontal asymptotes, if there is one.

f(x) = (x^2 +7x +12)/(x^2 -2x -24 )

= (x^2 +3x +4x+12)/( x^2 -6x +4x -24)

= (x+3)(x+4)/(x-6)(x +4)

Vertical asymtote : x = 6 ; x = -4

Holes : x = 6 ; x = -4

Horizontal asymtote :

y = x^2/x^2

y = 1