Hello Aaron, there are different philosophies how symbolics are handled. 
One goes towards structure-transformations to get a quick answer, the other 
towards being more expressive about the problem itself. However, I think 
maxima doesn't help you much here. I've typed up a short SymPy worksheet 
that shows you a few computations. In particular, note that simplifications 
of expressions are disabled and solveset "correctly" shows you that there 
is no solution. In other instances, it gives you all solutions as a set.

Key elements:

sympify('x^2 / x', evaluate=False)

 → x²/x

solveset(x²/x)

→ ø

solveset(sympify('(x^3 - x^2 - 6*x) / x', evaluate=False))

 → {-2, 3} but not "0"

Worksheet: 
https://cloud.sagemath.com/projects/14eed217-2d3c-4975-a381-b69edcb40e0e/files/scratch/sympy.sagews

-- Harald

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