Hi tinhnho
(t+1)/(t+4)^2 = K1/(t+4) + K2/(t+4)^2
Continue by multiplying both sides by (t+4)^2:
t+1 = K1*(t+4) + K2
t+1 = (K1*t) + (4K1 + K2)
Equating coefficients for t, we have
K1 = 1
Equating constant coefficients, we have:
4K1 + K2 = 1
4 + K2 = 1
K2 = 3
Thus, the partial fraction representation is:
f(t) = 1/(t+4)  3/(t+4)^2
Mathematica agrees.
