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

Posted 1 year ago
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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?

6 Replies

Aren't they equivalent?

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

Why is x=0 not a solution?

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

Out[3]= 1

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

Crossposted here.

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