Exercise 2, § 3

a) Let K be a commutative field and u = a_m X^m + a_{m+1} X^{m+1} + \ldots + a_n X^n a polynomial of K[X] such that a_m \neq 0, a_n \neq 0 (0 \leq m \leq n). Show that if g is a rational fraction of degree d \neq 0 in K(X), then u(g) is non-zero and is of degree nd if d > 0, and of degree md if d < 0. b) Deduce that a non-constant rational fraction g of K(X) is substitutable in every rational fraction of K(X) (observe that if g is of degree 0, there exists a \in K such that g - a has degree < 0).