partial fraction/ laplace

Let A/s^3+B/s^2+C/s+D/(s-4)=(s-2)/[s^3(s-4)]

Multiply both sides by s^3 and let s->0 =>A=1/2
Multiply both sides by s-4 and let s->4 =>D=1/32

Now 1/[2s^3]+B/s^2+C/s+1/[32(s-4)]=(s-2)/[s^3(s-4)]

Multiply both sides by s and let s->infinity
=>0+0+C+1/32=0
=>C=-1/32

Finally, sub. s=1 into the new equation, we have
1/2+B-1/32-1/96=1/3
B=-1/8

So, 1/[2s^3]-1/[8s^2]-1/[32s]+1/[32(s-4)]=(s-2)/[s^3(s-4)]

You can check the answer by sub. some other values of s.