Let $F$ be a field. Denote $R = \{ f/g \mid f, g \in F[x], g\neq 0 \}$, which is the fraction field of $F[x]$. Choose an element $a \in F$ and set $R_a = \{ f/g \in R\mid g(a) \neq 0 \}$.
Show that $R_a$ is a principal ideal domain, and describe all ideals of $R_a$.