Field of fractions of $R[X]$ Let $R$ be a domain and let $Q$ be its field of fractions. Show that the field of fractions of $R[X]$ is isomorphic to $Q(X)$. 
By the way, I don't know exactly what $Q(X)$ is. It means $Q[X]$? Or $Q$ times the ideal generated by $X$ in $R[X]$?

Generally, $A[\alpha]$ means "the ring generated by A and $\alpha$", and $A(\alpha)$ means "the field generated by A and $\alpha$". I have only ever seen the latter when $A$ itself is a field.
In the case of an indeterminate variable $X$, $A[X]$ would be the ring of polynomials (with coefficients in $A$), and $A(X)$ would be the fraction field of $A[X]$: the field of rational functions (with coefficients in $A$).
