\frac{q^2+11q+24}{q^2-5q-24}
To simplify the given expression, we can try factoring the numerator and denominator.
The numerator, $q^2+11q+24$, factors as $(q+3)(q+8)$.
The denominator, $q^2-5q-24$, factors as $(q-8)(q+3)$.
Now we can rewrite the expression in factored form: $$\frac{(q+3)(q+8)}{(q-8)(q+3)}$$
Notice that the factor $(q+3)$ appears in both the numerator and denominator. We can cancel out this common factor, resulting in: $$\frac{(q+8)}{(q-8)}$$
Thus, the simplified expression is $\boxed{\frac{q+8}{q-8}}$.
what can this expression not equal?
The expression $\frac{q+8}{q-8}$ can equal any real number except when the denominator, $q-8$, equals zero.
This means that the expression is undefined when $q=8$. Therefore, the expression cannot equal any real number when $q=8$.