Is the ring $\mathbb{Q}[X,Y,X^{-1}]$ isomorphic to $\mathbb{Q}[X]$ ?
I think of the first ring as the localisation of $\mathbb{Q}[X,Y]$ at $S=\{1,X,X^{2}...\}$. In my opinion, the localisation makes $X$ invertible and hence, the $X$ should get canceled out.