If I understood your description, the function should be as follows:
f(x) = (x²-2x-8)/(12x+24), if so then let's study the denominator (12x+24)
f(x) is defined for all values except those that give to the denominator the value of ZERO. Then 12x+24 ≠ 0 or 12x ≠ - 24==> x ≠ -2
f(x) is undefined & discontinued at x=-2
