In Section 6.2 of Nicholson: Introduction to Abstract Algebra, Exercise 31 reads as follows:

Let $\displaystyle E \supseteq F $ be fields and let $\displaystyle u \in E $ be transcendental over F.

(a) Show that $\displaystyle F(u) = \{ f(u){g(u)}^{-1} \ | \ f,g \in F[x] ; g(x) \ne 0 \} $

(b) Show that $\displaystyle F(u) \cong F(x) $ where F(x) is the field of quotients of the integral domain F[x].

(c) Show that every element $\displaystyle w \in F(u), w \notin F $, is transcendental over F.

Can someone help me approach this problem.

Peter