Assume $k$ is an algebraically closed field, and $x$ and $y$ are transcendental over $k$. I want to compute the valuation ring of $F$, the field of fractions of the ring $A=k[x,y]/I$, where $I=\langle y^2-\prod_{i=1}^n(x-i)\rangle$, which is pole of $x$, explicitly.
I think I have to take a leaf of the case rational function field but I couldn't. If someone helps me with it I will be happy.