To solve the given equation, we need to first combine the terms:

(2x + 3)/(x^2 - 2x) - (x + 3)/(x^2 + 2x) = 0

Now, let's find a common denominator for the fractions:

[(2x + 3)(x + 2) - (x + 3)(x - 2)] / [(x^2 - 2x)(x + 2)] = 0

Expanding the numerator:

(2x^2 + 4x + 3x + 6) - (x^2 - 2x + 3x - 6) = 0

2x^2 + 7x + 6 - x^2 + x - 6 = 0

x^2 + 8x = 0

Factoring out x:

x(x + 8) = 0

This gives us two solutions:

x = 0, x = -8

Therefore, the solutions to the equation are x = 0 and x = -8.