Comment #19 on issue 1694 by nicolas.pourcelot: solve has many issues with  
fractions
http://code.google.com/p/sympy/issues/detail?id=1694

Thanks Chris for your comments, even if I disagree with some ;)

1) I think checksolution() should clearly indicate when it can not  
conclude, either
by returning None (like .is_real, .is_positive, or is_zero do), or by  
returning
NotImplemented. Returning False or True when it can't conclude is imo not  
option, and
I can't assume that checksolution() will become good enough to conclude in  
any case ;)

2) Indeed. Substitution, expanding, and then simplifying. Or, better then,  
I'll have
a look at simplify, to simplify step by step.

3) No, -1 is *not* a solution of this equation, since x/(1+x) is not  
defined for x =
-1. It is however a solution of the equation after simplification, but it's  
not the
same. I suspect you're a physicist ;)
(Nor should 0 be a solution of x^2/x=0, but sympy simplifies x^2/x in x  
without
assuming x != 0)

4) Well, I thought about it, but I must admit I didn't want to spend too  
much time on
this patch (I just wanted to patch a few things I needed for my own work).  
Ok, I'll
try to do it.

5) Ok, done.

6) I didn't inspect existing test, I expect them to be all right.

>>> complex((x**Rational(1,2)+x**Rational(1,3)+x**Rational(1,4)).subs(x,  
>>> -9.5 - 2.8*I))
(3.0367413036900337-6.0250802087551731j)

Yes, you're right, 0 seems to be the only solution.
However, I think this is unrelated to this issue, so it may be solved as  
you sayed in
another patch (unless, of course, we choose to check every solution of  
solve(), in
every strategy and every case)... but I don't think it's the right thing to  
do).

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