Give an example of fields $k\subseteq K\subseteq L $, and $l\subseteq L$, for which $l/k$ and $L/K$ are algebraic, $k$ is algebraically closed in $K$, and $lK = L$, but $l$ is not algebraically closed in $L$.
This question has already been posted here $k$ is algebraically closed in $K$, and $lK=L$ , but $l$ is not algebraically closed in $L$., but has not yet had an answer, the truth is that I can not find such an example, could someone please help me? Thank you very much.