## Calculus 8th Edition

The domain is $$\mathcal{D}=\{(x,y)|y\neq-x\}.$$ It is shown in the figure below. The domain is in light blue and the red line is excluded from it.
The only constraint we have is that the denominator has to be different than zero which gives $x+y\neq0$ or $y\neq-x$, so the domain $$\mathcal{D}=\{(x,y)|y\neq-x\}$$ is the $xy$ plane with the line $y=-x$ excluded, and it is sketched in the figure below (the red line representing $y=-x$ is excluded, the region is light blue).