Partial Fraction of 1/(s^2(s+2))

Question

1/S²(S+2) Solve as soon as possible .........................

Answer 1

1 / [s²(s+2)] = A/s + B/s² + C/(s+2)

Multiply through by s²(s+2):

1 = As(s+2) + B(s+2) + Cs²

0s² + 0s + 1 = (A+C)s² + (2A+B)s + 2B

Equating coefficients of like powers, we get:

A + C = 0

2A + B = 0

2B = 1

So, B = 1/2, A = -1/4, C = 1/4

Thus, 1 / [s²(s+2)] = (-1/4) / s + (1/2) / s² + (1/4) / (s+2)