problem with solving inequality $x+1/x>-1+1/x$. different answer in Mathematica and Wolfram Alpha

I tried to solve inequality $$x+1/x>-1+1/x$$ with Wolfram Alpha, and it gave me the answer $$(-1,0)\cup(0,+\infty)$$. This is correct.

But when I try to solve it in Wolfram Mathematica 12.0 (with Wolframscript) it gives me an answer $$(-1,+\infty)$$ – with zero inside the answer – this is wrong.

I used this command in Wolframscript: Reduce[x+1/x>-1+1/x,x,Reals].

What's wrong with my script command?

• I think this is more of a mathematical question than a Mathematica question. In some sense you're right that $x=0$ shouldn't be considered a valid solution; on the other hand, if we just assume that $1/x$ is a symbol (even if it's infinite at $x=0$), then we can cancel it on both sides (since it's the same symbol). It's quite a matter of precise definitions to judge what's correct here. – Roman Feb 15 at 17:13
• Possibly related: mathematica.stackexchange.com/questions/211272/… -- Consider telling Wolfram Support and reporting back here what they say. – Michael E2 Feb 15 at 17:42
• Workaround: Reduce[# && FunctionDomain[List @@ #, #2], #2, Reals] &[ x + 1/x > -1 + 1/x, x] – Michael E2 Feb 15 at 17:46
• Crossposted here. – Rohit Namjoshi Feb 15 at 22:16
• Reduce and even Solve seem to not check the domain of the conditions, so it seems for now always explicitly give the domain if there are punctures in your definition. – user13892 Feb 16 at 23:26