let $L/K$ be an algebraic field extension. denote by $K(T)= Frac(K[T])$ the transcendental field extension of $K$. I would like to find out how to show that the equation $$K(T) \otimes_K L = L(T)$$
holds and especially where the requirement that $L$ algebraic flows in. That seems to be essential since for transcendent $L:= K(T)$ the formula above fails since $K(T) \otimes_K K(T)$ is not a field.
Thanks in advance!