I have a couple of questions I'm hoping someone can help me with. I'm using partial fractions to transfer a couple of equation from F(s) to f(t).

First question is:

F(s) = 4/s^2(s+1)(s+2)

By equating coefficients this becomes: 4/s^2(s+1)(s+2) = A/s + B/s^2 + C/(s+1) D/(s+2)

By multiplying by the numerator the equation becomes 4= As(s+1)(s+2) + B(s+1)(s+2) + Cs^2(s+2) + Ds^2(s+1)

Getting B,C & D is enough enough by substituting s=0,-1&-2. The answer I have for getting A I just don't understand, it says equate coefficients of s so that:

0=2A + 3B

I just don't see where this comes from.

Second question is to do with a closed loop control system. Using a standard control loop equation I have G(s)/1+ G(s).H(s)

This then becomes: (s/s+2) / [1+ 4.(1/s+2)] I have the answer as 2/s+10. I'm useless at working out fractions like this so any help would be appreciated.

I'm sure it's really basic stuff but I'm going number blind at this point. Thanks for your help.