Finding the domain of a three variable function I have a problem trying to solve the next excersice:
find the domain of the following function,
$f(x,y,z)=\frac{\sqrt{x^2z-3xz^2+3z^3}}{xy-x^2-y^2-1}$
I know that the domain should be:
$Domain=\{(x,y,z)|x^2z-3xz^2+3z^3 \geq 0\} \setminus \{(x,y,z)|xy-x^2-y^2-1 = 0 \} $
The thing is I have some problems finding the x,y for which:
$xy-x^2-y^2-1 = 0$ , It seems like $xy-x^2-y^2-1\neq0$ for all $x,y \in R$, but again I have some problems given the right argument.
I know it might seems a bit easy but I've been struggling for some time with this.
I would really apreciate any advice or hint you can give me.

Note that we can write
$$\begin{align}
xy-x^2-y^2-1&=-(x-y/2)^2-3y^2/4-1\\\\
&\le -1\end{align}$$
for all $x$ and $y$.  
Hence the denominator of $f(x,y,z)$ can never be zero.
