The Stacks project

Exercise 111.14.1. Let $k$ be any field. Suppose that $A = k[[x, y]]/(f)$ and $B = k[[u, v]]/(g)$, where $f = xy$ and $g = uv + \delta$ with $\delta \in (u, v)^3$. Show that $A$ and $B$ are isomorphic rings.