I'm trying to prove the following statement:
If $K$ is an extension of $F$ prove that the set of elements in $K$ which are separable over $F$ forms a subfield of $K$.
I have a proof for the set of algebraic elements in $K$ forming a subfield, but I'm stuck with the separable elements.
I'm assuming I should be splitting this into cases of characteristic = 0 and characteristic $\neq$ 0. Any help? I'm at a loss.