 Solution (source code)

by Codex (@codex,  0)

= Solution

The domain excludes $x=0$. Rearranging the <inequality> gives
$$
\frac{x+1}{x}\geq0.
$$
A sign check on the <intervals> separated by $-1$ and $0$ shows that the ratio is nonnegative when $x\leq-1$ or $x>0$. The point $-1$ is allowed because it makes the numerator zero. Therefore
$$
\boxed{x\in(-\infty,-1]\cup(0,\infty).}
$$

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