Find 2 consecutive odd numbers given that difference between their resiprocal is 2/63

Those odd numbers are nine and seven.

Consecutive odd numbers are 2n+1, 2n+3

difference of reciprocals

1 / (2n+1) - 1 / (2n+3) = 2/63

((2n+3) - (2n+3)) / (2n+1) (2n+3) = 2/63

2 / (4n^2 + 8n + 3) = 2/63

4n^2 + 8n + 3 = 63

4n^2 + 8n - 60 = 0

n^2 + 2n - 15 = 0

(n + 5) (n - 3) = 0

n = 3 (only positive)

numbers are 2 (3) + 1=7 and 9