Currently I am learning control systems. I specifically find the mathematics very hard to understand.

For my exam I am practicing on this question: "Determine the transfer function of this circuit in the S-domain."

I came to here:

But after filling in the Z impendances, I make it a mess. Could you please explain me in steps how to solve this mathematically?

Thank you in advance for your help!

Currently I am learning control systems. I specifically find the mathematics very hard to understand.

For my exam I am practicing on this question: "Determine the transfer function of this circuit in the S-domain."

I came to here:

I don't know if it's correct and I don't know how to simplify this. Could you please explain me in steps how to solve this mathematically?

Thank you in advance for your help!