Proving the Algebraicity of u-1 over Field K in Extension Field F

[Daveyboy]

Homework Statement

K is a field, F is an extension field of K.
If u is algebraic over K, u an element of F, show u^-1 is algebraic over K

I'm trying to find a contradiction when I assume u^-1 is transcendental, but I am not getting very far... anything to steer me in the right direction.

 

[Dick]

Don't try and do it by contradiction. If u is algebraic then it's a root of a polynomial over K. Try and find a polynomial that u^(-1) satisfies. Here's an example. If u satisfies x^2+2x+3, I'm pretty sure u^(-1) will satisfy 1+2x+3x^2. Why?