Let $K$ be a subfield of a field $K'$ and suppose we have an embedding $\phi:K \rightarrow L$ of $K$ into an algebraically close field $L$. Let $x \in K'$. If $x$ is algebraic over $K$, then we can extend $\phi$ to $K(x)$. What if $x$ is transcendental over $K$? Can we then extend $\phi$ to $K(x)$?