The question is asking to prove that Q \ Z is countable. We are allowed to use the fact that Q and N have the same cardinality.
My current idea is to show that there is a bijection between the set Q \ Z and Q and from there use the fact that the composition of the bijections between Q \ Z and Q and Q and N is bijective to show that Q \ Z has the same cardinality as N hence is countable.
However, I'm struggling to think of formally constructing a bijection from Q\Z to Q. Could someone help me with this? Or ss there a better way to do this question