#### Answer

$D=$ {$(x,y) | x \neq 0,y \neq 0$}

#### Work Step by Step

As we are given that $h(x,y)=\dfrac{e^x+e^y}{e^{xy}-1}$
The function $h(x,y)=\dfrac{e^x+e^y}{e^{xy}-1}$
represents a rational function which is continuous on its domain $D$.
Thus,
$ e^{xy}-1 \neq 0$
or, $e^{xy} \neq 1$
This means that $x \neq 0,y \neq 0$
Hence, Domain: $D=$ {$(x,y) | x \neq 0,y \neq 0$}