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

Posted 1 month 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?
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Posted 1 month ago
 Aren't they equivalent?
Posted 1 month ago
 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
Posted 1 month ago
 Why is x=0 not a solution? In[3]:= Limit[(x + 1/x) - (-1 + 1/x), x -> 0] Out[3]= 1 
Posted 1 month ago
 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
Posted 1 month ago
 Crossposted here.
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