In the equation 1/j + 1/k = 2/3, both j and k are positive integers. What is the sum of all possible values for k?
1/j + 1/k = 2/3
( j + k) / jk = 2/3
j + k = (2/3)jk
3 ( j + k) = 2jk
3j + 3k = 2jk
3k = 2jk - 3j
3k = j ( 2k - 3)
j = 3k / ( 2k - 3)
k j
2 6
3 4
6 2
Sum ok all possible values of k = 11
