Partial fraction

let (3s^2 + 4) / ((s+1)(s^2 + 1)) = A / (s+1) + (Bs +C) / (s^2 +1)

Then by comparing coefficient, we have
A+B = 3
B + C = 0
A+C = 4

Thus,
A = 7/2
B = -1/2
C = 1/2

Therefore,
(3s^2 + 4) / ((s+1)(s^2 + 1)) = [7 / (s+1) + (-s +1) / (s^2 +1)] / 2