X+8

____
x2 + 11x +24

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To simplify the expression (x+8)/(x^2 + 11x + 24), we need to factor the denominator and then simplify the fraction if possible. Here's how:

Step 1: Factor the denominator (x^2 + 11x + 24):
The denominator is a quadratic expression. We need to find two numbers that sum up to 11 and multiply to 24. The numbers that satisfy this condition are 3 and 8 because 3 + 8 = 11 and 3 * 8 = 24. So, the factorization is:
x^2 + 11x + 24 = (x + 3)(x + 8).

Now, the expression simplifies to:
(x + 8)/(x + 3)(x + 8).

Step 2: Simplify the fraction expression:
Since we have (x + 8) in both the numerator and denominator, we can cancel them out, leaving us with:
1/(x + 3).

Therefore, the simplified expression is 1/(x + 3).