Question

for what value of x is the rational expression below undefined?
check all that apply 
x+8/x^2-2x-24
A.4
B.-4
C.-6
D.-8
E.8
F.6

Answer 1

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).