simplify the sum
(w^2 + 2w - 24)/(w^2 + w - 30) + 8/(w - 5)
To simplify the sum, we need to find a common denominator for the two fractions. The common denominator in this case is (w + 5)(w - 6).
Now, we need to rewrite each fraction with the common denominator:
[(w^2 + 2w - 24)/(w^2 + w - 30)] + [8/(w - 5)] = [(w^2 + 2w - 24)/((w + 5)(w - 6))] + [(8(w + 5))/((w + 5)(w - 6))]
Now that they have the same denominator, we can combine them:
[(w^2 + 2w - 24 + 8(w + 5))/((w + 5)(w - 6))] = [(w^2 + 2w - 24 + 8w + 40)/((w + 5)(w - 6))] = [(w^2 + 10w + 16)/((w + 5)(w - 6))]
Therefore, the simplified sum is (w^2 + 10w + 16)/((w + 5)(w - 6)).