simplify the sum
w^2 + 2w - 24/w^2 + w - 30 + 8/w - 5
(w + 6)(w - 4)/(w + 6)(w - 5) + 8/(w - 5) - 5
(w - 4)/(w - 5) + 8/(w - 5) - 5
Since the denominators are the same, we can combine the fractions:
(w - 4 + 8)/(w - 5) - 5
(w + 4)/(w - 5) - 5
(w + 4 - 5(w - 5))/(w - 5)
(w + 4 - 5w + 25)/w - 5
(-4w + 29)/w - 5