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