# Partial Fractions/Laplace Transforms

1. Dec 4, 2005

### mpm

I have the transfer function X(s) = (18s+10)/(s(3s^2+18s+10))/

I need to break it up into partial fractions so i can take the Lapalce transform and get it into a response.

I cant figure out what it breaks up into though. I know its 3 partial fractions and one of which is 1/s I believe. But Im not sure about the other two.

Can someone help me with this so maybe I can find the laplace transform of it?

Thanks

2. Dec 4, 2005

### benorin

break-up X(s) by partial fracs using

$$X(s)=\frac{A}{s} + \frac{B}{s+3-\frac{\sqrt{51}}{3}}+ \frac{C}{s+3+\frac{\sqrt{51}}{3}}$$

solve to get A=3, B=nasty, C=also_nasty

3. Dec 5, 2005

### Tide

This may help:

$$\frac {1}{s(s-a)(s-b)} = \frac {1}{ab} \cdot \frac {1}{s} + \frac {1}{a(a-b)} \cdot \frac {1}{s-a} + \frac {1}{b(b-a)} \cdot \frac {1}{s-b}$$