Calculate the localization $S^{-1}R$ where $R=\mathbb{C}[x]$ and $S=\{f:f(0)f(1)\ne0\}$.
The problem isn't that I don't know how to solve it, but that I don't understand the question; A localization is defined by $\{f/g:f\in R, g\in S\}$ and $$a/b=c/d\iff\exists t\in R, 0=t(ad-bc)$$ (We can observe that $0\notin S$).
I don't really understand what should I calculate: In my eyes the localization is exactly $$\{f/g:f\in R, g\in S\}$$