"Nasser M. Abbasi" schrieb:   
   >   
   > On 10/4/2017 11:21 AM, clicliclic@freenet.de wrote:   
   >   
   > > I believe that:   
   > >   
   > >    SQRT(x^2/(1 + SQRT(x^2 - 1))^2)*(1 + SQRT(x^2 - 1))/x = x/SQRT(x^2)   
   > >   
   > > FriCAS will probably squeal, but can Mathematica or Maple validate   
   > > or invalidate this simplification?   
   > >   
   >   
   > 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   
   >   
      
   Holy Wolfram. On Derive, equality also holds for -1 < x < 1:   
      
   VECTOR(SQRT(x^2/(1 + SQRT(x^2 - 1))^2)*(1 + SQRT(x^2 - 1))/x   
    = x/SQRT(x^2), x, -2, 2, 1/10)   
      
   [true, true, true, true, true, true, true, true, true, true, true,   
    true, true, true, true, true, true, true, true, true, true, true,   
    true, true, true, true, true, true, true, true, true, true, true,   
    true, true, true, true, true, true, true, true]   
      
   where the case of x = 0 works because ? = ? is true on Derive.   
      
   Martin.   
      
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