## Calculus: Early Transcendentals 8th Edition

The domain of the given function is $$\left\{(x, y) | x \ne -y \right\}.$$
$$g(x,y)=\frac{x-y}{x+y}$$ This function is defined only when: $$x+y \ne 0$$ $\Rightarrow$ $$x \ne -y$$ Therefore, the domain of the given function is $$\left\{(x, y) | x \ne -y \right\}.$$