What are the discontinuities of the function f (x) = x^2+2x-8/12x+24?

Factor the numerator and denominator of the function to find holes, vertical asymptotes, and horizontal asymptotes.

Numerator: (x - 2) (x + 4)

Denominator: 12 (x + 2)

This would mean there is infinite discontinuity at x = - 2 (the vertical asymptote).