$f(x)=x/1$ is not injective? In chapter 3 of Atiyah and Macdonalds Intro to Comm Algebra there is the statement
"We also have a ring homomorphism $f:A\rightarrow S^{-1}A$ defined by $f(x)=x/1$. This is not in general injective." (Note: $A$ denotes an integral domain and $S$ a multiplicatively closed subset of $A$.)
How could this possibly not be injective? If $f(x)=f(y)$ then $x/1=y/1$ so $1x=1y$ hence $x=y$. What am I missing here?

Note
If $x \in R$ and $s \in S$ are such that $xs=0$ then we have 
$$\frac{x}{1}=0=\frac{0}{1}$$
