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The reported bug can be reproduced in conda-installed Sage 10.5 on Linux Mint.
Simpler trigger:
sage: R = PolynomialRing(QQ, 'x')
sage: R.inject_variables(verbose=False)
sage: S = PolynomialRing(R, 'u, v')
sage: S.inject_variables(verbose=False)
sage: d = u - 1
sage: f = 1 / x * d
sage: f / d
Traceback (most recent call last):
...
ZeroDivisionError: fraction field element division by zero
