1 A B
________ = _____ + _________
k ( k + 3) k k + 3
We can use the method of partial fractions to solve this
Mutilply through by k ( k +3) and we have
1 = A( k + 3) + Bk simplify
1 = (A + B)k + 3A equate terms and we have this system
A + B = 0
3A = 1 ⇒ A = 1/3
Which means that B = -1/3
So (A, B) = (1/3, -1/3 )