Okay it has nothing to do with function fields, is just that function field 
passes the computation to fraction_field:

sage: k = FiniteField(nicePrime)
kA.<a> = PolynomialRing(k)
ka = kA.fraction_field()
kaX.<X> = PolynomialRing(ka)
kax = kaX.fraction_field()
sage: kax
Fraction Field of Univariate Polynomial Ring in X over Fraction Field of 
Univariate Polynomial Ring in a over Finite Field of size 13
sage: kax(2)/kax(2)
2/2
sage: ka(2)/ka(2)
1



בתאריך יום ראשון, 1 באפריל 2012 20:25:45 UTC-6, מאת syd.la...@gmail.com:
>
> I'm working on this but I thought maybe someone like William who wrote the 
> function field module knows the fix immidiately:
>
> sage: k = FiniteField(13)
> kA.<a> = PolynomialRing(k)
> ka = kA.fraction_field()
> kx.<x> = FunctionField(ka)
>
> sage: ka(2)/ka(2)
> 1
> sage: kx(2)/kx(2)
> 2/2
>
> It makes some functions that clear denominator, delussional.
>
>

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