smc

Moving all variables to one side of the equation, we can use Simon's Favorite Factoring Trick to factor the equation into $$(x+1)(y-1)=-1$$ Plugging in $-1$ and $1$ as the $x$ and $y$ sides respectively, we get $x=-2$ and $y=2$. Plugging this in to $\frac{1}{x}-\frac{1}{y}$ gives us $\boxed{-1}$ as our final answer.