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.