Solving a Complex Circuit Equation

[jonlg_uk]

Homework Statement

I have the following circuit...

I have managed to derive an equation for U2:

Now I want to substitute U2 into U1, in order to derive equation for U1

I have defined U1 as:

Now I substitute U2 into the above equation. This is how far I get...I am stuck...


My circuit simulator is saying that U1 is equal to:

However I cannot simply to get this equation. Can someone please help I have spent hours trying to get U1 to look like the U1 that the simulator produces.


I thank you in advance.

 

[jonlg_uk]

Wow 380 hits and no-one can solve it. I was up until 3am last night trying to do this and still couldn't get U1 looking like the simulator produced. I would be massively grateful if someone, with better mathematical skills than me have a go at solving this, its driving me BONKERS.