Let $E$ and $F$ be subfields of some larger field $K$. If an element $x \in K$ is both separable over $E$ and separable over $F$, is $x$ separable over $E \cap F$?
Edit: Here, I am assuming $K$ is algebraic over both $E$ and $F$. When I say $x$ is separable over a field, I mean that its minimal polynomial over that field is separable.
Also, I'm new to this. Can someone tell me why my original question was voted closed?
There isn't really any context behind this question; it's just something I was wondering about and made basically no progress on in either direction. I couldn't find it online already, so I figured I would ask it here in case anyone has seen it before.