Problem with solving inequality x+1/x>-1+1/x

Questions
1

Wolfram|Alpha gives correct answer (-1;0)(0;+infty).
But wolfram script gives (-1;+infty) – so, with 0 inside answer.

I use this command: Reduce[x+1/x>-1+1/x, x];

Where is a problem with my Wolfram script?

2

Aren’t they equivalent?

3

in very high level difficulty are in inequality. to find some method to use.
Degreaser

4

Hi,

this one appears to work:

Reduce[x + 1/x > -1 + 1/x && FunctionDomain[{x + 1/x, -1 + 1/x}, x],x]

The result correctly excludes x==0 as a solution.

Cheers,

Marco

5

Why is x=0 not a solution?

In[3]:= Limit[(x + 1/x) - (-1 + 1/x), x -> 0]

Out[3]= 1
6

Hi Frank,

because the expression is not defined at x=0. You cannot substitute x->0 because you would divide by zero. The limit that you calculate does exist. If you run:

FunctionDomain[(x + 1/x), x]

You obtain:

x < 0 || x > 0

The function is not defined for x=0. Hence, x=0 cannot be a solution of the inequality.

Cheers,

Marco

7

Crossposted here.