Let $K$ be an extencion of $F$ and let $a,b\in K$. If $a$ is not algebraic in $F$, but it is in $F(b)$, show that $b$ is algebraic in $F(a)$
If $v$ is algebraic over $K(u)$, for some $u\in F$, and $v $ is transcendental over $K$, then $u$ is algebraic over $K(v)$