What is the sum?

3/x^2-9 + 5/x+3

A) 8/x^2+x-6

B) 5x-12/x-3

C) - 5x / (x+3 (x-3)

D) 5x-12/x+3 (x-3)

We will use the formula a^2-b^2 = (a-b) (a+b) to get the fractions to the same dominator.

3/[ (x-3) (x+3) ]+5 / (x+3) =

3/[ (x-3) (x+3) ]+5 (x-3) / (x+3) [ (x-3) (x+3) ] =

(3+5x-15) / [ (x-3) (x+3) ] =

(5x-12) / [ (x-3) (x+3) ]

The final answer is D.