Simplify the complex fraction.

N-6/n^2+11n+24/n+1/n+3

A - (n-6) (n+1) / (n+3) ^2 (n+8)

B - (n-6) (n+8) / (n+1) (n-8)

C - (n-6) (n+1) / (n+3) (n+8)

D-n-6 / (n+1) (n+8)

N-6/n²+11n+24/n+1/n+3

First, we need to factor the following:

n² + 11n + 24 → (n + 3) (n + 8)

n² → n * n

factor of 24 are:

1 x 24

2 x 12

3 x 8 We will use these factors. 3 + 8 = 11

4 x 6

Division involving fractions results to multiplying the first fraction to the reciprocal of the second fraction.

n-6 / (n+3) (n+8) * n+3 / n+1 → n+3 is in both numerator and denominator. Cancel each other out.

n-6/n+8 * 1/n+1

n-6 / (n+8) (n+1) Correct answer is Choice D.