AUSTRIAN-POLISH 1978 Problem 4

Let $c\neq 1$ be a positive rational number. Show that it is possible to partition $\mathbb{N}$ , the set of positive integers, into two disjoint nonempty subsets $A,B$ so that $x/y\neq c$ holds whenever $x$ and $y$ lie both in $A$ or both in $B$ .