Simplify Equation

[Delfad0r]

Consider the following:

>>> x, y, z = symbols('x y z', positive = True)

>>> equation = Eq(x*y*(x**5-x-y)*(x-y)/2,0)

My goal would be reducing `equation` to something like

(x**5-x-y)*(x-y)==0

removing the nonzero factors, but `simplify(equation)` doesn't work (and I think it isn't supposed to work like that).

Ideally, I would also like to be able to further reduce `equation` by assuming, for instance, that `x!=y`; in this case, `equation` should reduce to

x**5-x-y==0

So, what I'm trying to do is reducing `equation` without actually solving it, and I can't find any function that does that.

Any help would be greatly appreciated.