I want to check that $F(a,b)/F(1/ab,a+b)$ is an algebraic extension, where $a,b$ are nonzero elements of $E$, where $E/F$ is field extension.
I don't mean full solution, but I want some hint.. I think this problem much time, but there aren't any good ideas :( But if you give solution, it's good, too!
If you suggest some hint, or idea, then I will appreciate very much!
Removed: the hint of Richard James is better than my answer.