Using Laplace, getting stuck on decomposition

I think I have a fair idea of how to solve my equations, using Laplace transform. But the partial fraction decomposition seems to elude me...

I get X and Y as such.

I get this:

I pulled the handbrake here because wolfram alpha got something else...

Wolfram Alpha, see: Partition fraction expansion

If anyone could find it in their heart to ease me throw this one, so that I can solve my system of differential equations...

Re: Using Laplace, getting stuck on decomposition

Your answer can't be right because:

which is different from the original given .

We have

If we proceed:

This means: , , and

Can you proceed?

Re: Using Laplace, getting stuck on decomposition

Thank you very much! I got it from here. I didn't write the proposed denominators correctly.