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