Partial fractions (for laplace)

1. Dec 13, 2009

bakin

1. The problem statement, all variables and given/known data
This problem is killing me.

I need to bust this thing up using partial fractions.

2. Relevant equations

3. The attempt at a solution

I'm leaning towards it being separated like this. Is this correct?

If it is, I'm not exactly sure what I'm supposed to do next.

Last edited: Dec 13, 2009
2. Dec 13, 2009

rootX

145s/ [(s+2j)(s-2j)(s-2+3j)(s-2-3j)]
Make sure above is correct .. now

[145s / (s-2j)(s-2+3j)(s-2-3j) ]*1/ [(s+2j)]
+
[145s / (s+2j)(s-2+3j)(s-2-3j) ]*1/ [(s-2j)]
+
[145s / (s-2j)(s+2j)(s-2-3j) ]*1/ [(s-2+3j)]
+
[145s / (s-2j)(s+2j)(s-2+3j) ]*1/ [(s-2-3j)]

I believe what I did above should be self explanatory. Now next step is to substitute s=-2j to [145s / (s-2j)(s-2+3j)(s-2-3j) ]
s=2j to [145s / (s+2j)(s-2+3j)(s-2-3j) ]
s = 2-3j in the third, and s=2+3j .. so on, You leave one of the simplest possible factor in the denominator taking all others to the numerator and then substituting the root.

See if that works

3. Dec 13, 2009

bakin

I'll try that, thanks

4. Dec 13, 2009

rootX

Answering your question in the OP, you had that correct. But, I just wanted to share a new tool I discovered in Calc III class which I think is very helpful for partial fractions.