Let the smaller of the two odd integers be n, such that the larger one is n + 2
(1/n) + (1/(n + 2) = (12/35)
((n + 2 + n)/(n(n+2)) = (12/35)
((2n + 2)/(n(n+2)) = (12/35)
Equating the numerators both sides give: 2n + 2 = 12
2n = 12 - 2 = 10
n = 5
Therefore the greater of the two integers is n+2 = 5 + 2 = 7.