Answer
The Domain is the set of all ordered pairs $(x,y)$ such that $x\neq y$.
The Range is given by
$$z\in (-\infty,\infty) = \mathbb{R}$$
i.e. the set of all real numbers.
Work Step by Step
1) Domain
Here we have the restriction that the denominator must be different than zero. This means that $x-y\neq 0\Rightarrow x\neq y$. All other values for $x$ and $y$. We will denote the set of all ordered pairs $(x,y)$ such that $x\neq y$ by $s=\{(x,y)|x\neq y\}$ and this set is the domain of this function:
$$(x,y)\in s.$$
2) Range
In the numerator, we have the product of two numbers $xy$ and they have to be different than each other but still, that product can take any real value. So we end up dividing any real number by any real number different than zero which can as a result give any real number so we see that the range is
$$ z\in (-\infty,\infty) = \mathbb{R}.$$
