Qing Liu-Corollary 2.15

Question

In the book Algebraic Geometry and Aritmetic Curves of Qing Liu the author wants prove that if $\rho :A\longrightarrow B$ is flat (the $A$-algebra $B$ is flat), then for every prime ideal $\mathfrak{q}$ of $B$, $B_{\mathfrak{q}}$ is flat over $A_\mathfrak{p}$, where $\mathfrak{p}=\rho^{-1}(\mathfrak{q})$. In order to do this he claim that $B_{\mathfrak{q}}$ is a localization of $B\otimes_A A_\mathfrak{p}$. Can anyone explain this last fact?