I would like to get a reference of the following fact.

Let $A\subseteq B$ be affine domains over an algebraically closed field of characteristic zero. If $Q(A)$ is algebraically closed in $Q(B)$, show that any genral fiber of the associated morphism of schemes is irreducible, or in other words, there exists a non-empty open set $V$ in Max $A$, such that for any maximal ideal $\mathfrak{m}\in$ Max $A$, the extended ideal $\mathfrak{m}B$ is irreducible.

Thank you in advance.