Let $k$ be a field, $A = k[x,y] / (y^2, xy)$. I know that the ideals $P = (x-1)$ and $Q = (x-3)$ are maximal ideals in A, so $U = $ Spec $A \backslash \{ P, Q \}$ is an open subset of Spec $A$. Then it turns out that $$ \frac{x-2}{(x-1)(x-3)} $$ is an element of $\Gamma (U , O_{Spec \ A})$ and it is a rational function.
Could someone please explain me why this is a rational function? (I am reading the explanation in the notes by Ravi Vakil, but I am getting confused. Perhaps I am missing something easy...)
ps I would also appreciate if someone could explain me how this is an element of $\Gamma (U , O_{Spec \ A})$. I am a bit confused about this also.. Thank you!