The function field of $V=Z(y^2-x^3)$

Question

Let $k$ be a field and let $V=Z(y^2-x^3).$

Can someone explain to me why $k(V)\cong k(s,t)$ ??

with $t=x+(y^2-x^3),s=y+(y^2-x^3)\in A(V)=k[x,y]/(y^2-x^3).$

Can we generalize it : If $V=Z(f)$ with $f\in k[x_1,\dots,x_n]$ be an irreducible polynomial and $t_i=x_i+(f)$ then $k(V)\cong k(t_1,\dots,t_n).$

Thanks in advance.