3. Find all irreducible positive fractions that increase by 3 times when both the numerator and the denominator are increased by 12.

ANSWER: $2 / 9$.
Solution: Note that if the numerator is not less than 6, then by adding 12 to it, it will not increase more than three times, so the fraction itself certainly cannot increase three times. By trying numerators $1,2,3,4,5$, we get the fractions 1/3.6, 2/9, 3/18, 4/36, 5/90, among which only $2 / 9$ is irreducible.