I can only guess that by x^2-2x-24 you mean the entire denominator. In cases like this is is important to use parentheses to remove any doubts. For example:
(x+8) / (x^2-2x-24).
This rational expression is undefined at any x for which the denominator, x^2-2x-24, is zero.
x^2-2x-24 factors into (x+4)(x-6). The roots are -4 and +6.
Thus, the given expression is undefined at {-4,6} (set notation).
