Partial fractions (for laplace)

[bakin]

Homework Statement

This problem is killing me.

I need to bust this thing up using partial fractions.

Homework Equations

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.

 

[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

 

[bakin]

I'll try that, thanks

 

[rootX]

I'll try that, thanks

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.