Peter Luschny schrieb:   
   >   
   > Am Mittwoch, 4. Oktober 2017 18:38:49 UTC+2 schrieb Nasser M. Abbasi:   
   > >   
   > > Mathematica says, for real x, the above is valid only for x<=1 || x>=1   
   > >   
   > > In[1]:= expr1 = Sqrt[x^2/(1 + Sqrt[x^2 - 1])^2]*((1 + Sqrt[x^2 - 1])/x);   
   > > In[2]:= expr2 = x/Sqrt[x^2];   
   > > In[5]:= Reduce[expr1 - expr2 == 0, x, Reals]   
   > >   
   > > Out[5]= x <= -1 || x >= 1   
   >   
   > This depends on the method of verification.   
   >   
      
   I looked at the Mathematica documentation and found that adding Reals as   
   a third argument restricts not only the variables but also all function   
   values to real numbers. Real values of Sqrt[x^2 - 1] imply x^2 >= 1,   
   hence the omission of all x^2 < 1 from Nasser's result.   
      
   Nasser's query should therefore be restated as:   
      
     Reduce[expr1 - expr2 == 0 && ElementOf[x, Reals], x]   
      
   where "&&" and "ElementOf" must be replaced by proper Mathematica   
   keywords if my guesses happen to be off.   
      
   Martin.   
      
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