Field of fractions of a quotient ring

edit

I have a polynomial ring defined over another polynomial ring.

_.<a1,a2,a3,a4,a6> = PolynomialRing(RR)
PR.<x,y> = PolynomialRing(RR)

I defined a variable as follows.

x3 = (-x^3 + y^2)/x^2

What I want to do is to coerce this variable to a quotient ring so that the numerator of x3 becomes x and finally x3 becomes 1/x.

To do that, I tried to define a field of fractions over the quotient ring like this

_.<x,y> = Frac(PR.quo(y^2-x^3-x))

which has failed.

I was able to do it in Magma. I am new to Sage, so sorry if there is an obvious mistake.