Wolfram|Alpha shouldn't assume $x\neq 0$. It shouldn't claim $0/x=0$.

When you input 0/x on W|A, it claims, with no restrictions on x, that 0/x=0. While of course it claims 0/0 is indeterminate.

I’d like it to be more rigorous in this regard. It is typical for W|A to assume an unspecified letter x is a complex variable. In this case, as always, it should assume x is any complex variable, but it assumes x\neq 0, without pointing out the assumption. I’m honestly bothered by this.
[1]: 0/x - Wolfram|Alpha

The Generic and Non-Generic Cases tutorial in the Wolfram Language documentation center explains the motivation for this behavior.

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