To solve this equation, we can cross multiply:
(2a + 3c)(2b - 3d) = (2a - 3c)(2b + 3d)
Expanding both sides:
4ab - 6ad + 6bc - 9cd = 4ab + 6ad - 6bc - 9cd
Combining like terms: -6ad + 6bc = 6ad - 6b
c Adding 6ad to both sides: 6bc = 12ad - 6bc
Adding 6bc to both sides: 12bc = 12ad
Dividing both sides by 12: bc = ad
Therefore, the equation 2a + 3c / 2b + 3d = 2a - 3c / 2b - 3d is true if and only if a/b = c/d.