Let $U\subset V$ be two affine varieties.
Define the function field of an affine variety $X$ to be $$ k(X)=\operatorname{Frac}(A(X)) $$
How to show that $k(U)=k(V)$?
In particular, if $U=\mathbb{V}(x,y), V=\mathbb{V}(x)$, I cannot see them are equal. For example, $\frac{1}{y-1}\in k(X)$, but seems not in $k(Y)$.