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differences in Solve with -1/2 and -0.5


Can anyone give a good reason why there is a difference in the 
following?  Preferably one that my students will understand.

In[1]:=
Solve[D[x E^(-x/2), x] == 0, x]
Out[1]=
{{x -> 2}}
In[2]:=
Solve[D[x E^(-0.5*x), x] == 0, x]
General::dbyz:Division by zero.
Out[2]=
{}

Ken Levasseur
Math. Sciences
UMass Lowell


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