mersenneforum.org - View Single Post - Partial fraction of this expression?please!!

jinydu · 2005-01-17, 06:21

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.

2005-01-17, 06:21	#2
jinydu Dec 2003 Hopefully Near M48 2·3·293 Posts	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 = (K1t) + (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.