Suppose $A$ is an integral domain, with quotient field $K$, and let $L/K$ be an arbitrary field extension. If $B$ is the integral closure of $A$ in $L$, what is the quotient field of $B$?
If $L/K$ is algebraic, the argument in this question shows the quotient field of $B$ is $L$.
Example (d) on page 4 of Curtis and Reiner's Methods of Representation Theory Vol I says the quotient field of $B$ is $L$ for any field extension $L/K$, but I don't see a way to get a handle on showing any non-algebraic element of $L$ is a fraction of elements in $B$ without any polynomial relation to exploit.