Answer
$(-\infty,0)U(1,\infty)$
Work Step by Step
Step 1. The domain requirement(s) for this function is $\frac{x}{x-1}\gt0$
Step 2. Identify the boundary points $x=0,1$ and intervals $(-\infty,0),(0,1),(1,\infty)$
Step 3. Choose test values $x=-1,0.5,2$, test the inequality as get results $True,\ False,\ True$
Step 4. Thus we have the domain as $(-\infty,0)U(1,\infty)$
