Perform the indicated operations, then simplify.
(2y)/(y + 8) + (3y)/(y^2 - 64) - (4)/(y - 8)
A. (5y - 4)/(y^2 + 2y - 64)
B. (2y^2 - 17y + 32)/[(y - 8)(y + 8)]
C. (5y - 4)/[(y + 8)(y - 8)]
D. (2y^2 - 17y - 32)/[(y + 8)(y - 8)]
To perform the indicated operations, we need to find a common denominator for all the fractions. The common denominator will be (y + 8)(y - 8).
Now, let's rewrite the fractions using the common denominator:
(2y)/(y + 8) + (3y)/(y^2 - 64) - (4)/(y - 8) = (2y)/(y + 8) + (3y)/[(y + 8)(y - 8)] - (4)/(y - 8)
Next, let's combine the fractions with the common denominator:
= [2y(y - 8) + 3y - 4(y + 8)] / [(y + 8)(y - 8)]
= (2y^2 - 16y + 3y - 4y - 32)/[(y + 8)(y - 8)]
= (2y^2 - 17y - 32)/[(y + 8)(y - 8)]
So, the simplified form of the expression is (2y^2 - 17y - 32)/[(y + 8)(y - 8)].
The correct answer is D.