I don't think we'll ever get SR to operate properly in positive 
characteristics; especially because it would allow completely arbitrary 
characteristic combinations in the first place, but perhaps the cases below 
help in tracking down if we can so something to improve the situation a bit:

sage: ((1)*((1)*x+(1)/x)^3+(1)).expand()
x^3 + 3*x + 3/x + 1/x^3 + 1
sage: ((k(1)*x+k(1)/x)^3+k(1)).expand()
x^3 + 3*x + 3/x + 1/x^3 + 1
sage: (k(1)*(k(1)*x+k(1)/x)^3).expand()
x^3 + 1/x^3
sage: (k(1)*(k(1)*x+k(1)/x)^3+k(1)).expand()
0/x + 1/x^3 + 1
sage: ((k(1)*x+k(1)/x)^3+k(1)).expand()
x^3 + 3*x + 3/x + 1/x^3 + 1

so it's the combination of multiplying the third power by k(1) and adding 
k(1) to it that leads "expand" to producing an expression that is really 
invalid.

My guess is that it finds a nonzero factor 3 somewhere, which it assumes is 
invertible, and ends up multiplying both numerator and denominator of some 
fraction somewhere. The numerator ends up being combined in GF(3), so that 
one gets 0 and SR takes it happily from there, removing the factor 3 from 
the denominator again.

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