- #1

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If u is transcnedetal over F, it is routine to verify that:

F(u) = {f(u)g(u)^(-1) | f,g in F[x]; g /= 0}

However, me being the scrubbiest of all scrubs does not understand what they did here.

First of all, I don't understand why they needed to invert the g(u) function.

It goes on to say that F(u) is isomorphic to F(x), the field of quotients of the integral domain F[x].

Can somebody shed some light on this stuff for me?