Comment #2 on issue 2033 by asmeurer: solve should be able to handle rational function systems
http://code.google.com/p/sympy/issues/detail?id=2033
Well, the Groebner Basis method can handle polynomial systems in full generality, unlike your method, which will not always work. On the other hand, it can be slow sometimes, so I think maybe a preparser heuristic like that could be useful if it is significantly faster (although I would like convincing of this fact first, of course).
But either way, that is kind of separate from the issue here, which is just that solve() should multiply through by the denominator of a rational function before solving (and then check to make sure that none of the solutions make the original denominator zero at the end).
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