Answer
$\{x|x\lt 0\ or\ x\gt1 \}$.
Work Step by Step
The domain requirement(s) for the given function is $\frac{x}{x-1}\gt0$ with boundary points $x=0,1$. The "$\gt$" sign implies that the solution will be "outside" the region between the boundary points, thus $x\lt 0\ or\ x\gt1$ that is $\{x|x\lt 0\ or\ x\gt1 \}$.
