Answer:
possible digits: 0, 3, 6 or 9
Explanation:
To make the fraction reducible, the number in the denominator needs to have a common prime factor with the number in the numerator.
The number in the numerator can be factored in 3 * 5, so the denominator needs to be multiple of 3 or 5.
To be multiple of 5, the last number needs to be 0 or 5, which is not the case.
To be multiple of 3, the sum of the digits needs to be a multiple of 3.
The sum of the digits is 2 + x + 7, with x being the missing digit.
To have a multiple of 3, we have that x + 9 needs to be multiple of 3, so we can have x=0, x=3, x=6 or x=9, which would give us the fractions:
x=0: 15/207 = 5/69
x=3: 15/237 = 5/79
x=6: 15/267 = 5/89
x=9: 15/297 = 5/99