# Homework Help: Proof of an inverse Laplace Transform needed please

1. Apr 20, 2010

### raytrace

1. The problem statement, all variables and given/known data

$$\frac{s}{(s-a)(s-b)}$$

2. Relevant equations

Now I know that it results in:

[tex]\frac{ae^(at)-be^(bt)}{a-b}[\tex]

3. The attempt at a solution

OK, I don't have the slightest clue where to begin. Could someone point me in the right direction? I've looked at all the Transforms on the table on the back of the book but none of them give me a clue as to how to deal with a [tex]\frac{s}{s-a}[\tex] situation.

2. Apr 20, 2010

### Count Iblis

Evaluate the residues of

s/[(s-a)(s-b)] exp(st)

at s = a and s = b using L'Hôpital's theorem.

3. Apr 20, 2010

### raytrace

Thanks for the quick reply, will try that out.