(In reply to hmmmm
Well, if your point is that this problem is easy for a Russian IMO, I must agree.
However, I don't understand your proof.
(3n - 2)/(2n) = 3/2 - 1/n, but that doesn't make (3n - 2)/(2n) irreducible. In fact, (3n - 2)/(2n) is reducible for all even n.