FractionField does not reduce fractions correctly over some coefficient rings

[saliola]

Fractions are note reduced when dividing two monomials in a fraction field over a polynomial ring with coefficients in RR or CC. Here is a very simple example, but the problem persists for multivariate rings as well:

sage: F = RR['x'].fraction_field()
sage: F.inject_variables()
Defining x
sage: x/x        # this should be 1
x/x
sage: x.is_unit()
True
sage: ~x
1.00000000000000/x
sage: ~x * x     # this should be 1
x/x
sage: x/x == 1
True

Same problem occurs with CC, CDF, CIF, RDF, RIF, RBF, etc.

Component: algebra

Keywords: polynomials, fraction fields

Issue created by migration from https://trac.sagemath.org/ticket/32285