:
Multiply (each term) equation by 3AB, results
AB = 3B + 3A
:
Subtract 3B from both sides
AB - 3B = 3A
:
Factor out B
B(A - 3) = 3A
:
Divide both sides by (A-3)

B = 3a/a-3
:
Choose a value for A which will result in an integer
A = 4 is easy
B = 3 x 4 / 4 - 3
then
B = 12
Check solution in original equation
1/3 = 1/4 + 1/12
4/12 = 3/12 + 1/12