#### Answer

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.

#### Work Step by Step

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).