Simplify the sum.
(w^2 + 2w - 24/ w^2 + w - 30 ) + 8/ w - 5

The equation given in the question for simplification is

(w^2 + 2w - 24/ w^2 + w - 30 ) + 8/ w - 5 

Firstly let us simplify 
w^2 + 2w - 24 = w^2 + 6w - 4w - 24
                        = (w + 6)(w - 4)
Secondly let us simplify
w^2 + w - 30 = w^2 + 6w - 5w - 30
                     = (w + 6)(w - 5)
Then
(w + 6)(w - 4)/(w + 6)(w - 5) + 8/(w - 5)
=(w - 4)/(w - 5) + 8/(w - 5)
=(w - 4 + 8)/(w - 5)
= (w + 4)/(w - 5)

I hope the procedure is clear enough for you to understand and this is the answer that you were looking for and the answer has actually come to your desired help.

The answer is