Simplest way to attack this (i.e. how I would attack a similar problem at work).
1. Replace all devices with a general impedance (call it, for example, Z, so R1 = Z1, R2 = Z2, L = Z3, C = Z4.)
2. Solve the now trivial three-node voltage divider problem using KCL.
3. Replace all the Zs with their actual impedences (e.g. Z1 = R1, Z2 = R2, Z3 = sL, Z4 = 1/sC)
4. Simplify the expression and you're done!
That's not nice for the teacher to give you that problem without the proper background.
If you are only interested in this problem, use @analogdesign 's advice in post #6. But basic circuits is something you'll surely need in your career. It is worth your time to learn it. A very effective and fast way to learn is using Khan Academy. It takes less than 5 hours there to learn a whole basic circuits course.