To solve the equation, we need to find a common denominator for both sides.

Multiply both sides by 3(x+2)(x) to get rid of the fractions:

3(x+2)(x)(х+2/2) + 3(x+2)(x)(2/х) = (х+2)(x)(х+2/3) + (х+2)(x)(3/х+2)

Expand both sides:

3(x^2 + 4x) + 6(x^2 + 2x) = x^2(x+2/3) + 2(x^2+4x)

Simplify:

3x^2 + 12x + 6x^2 + 12x = x^3/3 + (2x^2 + 8x)

9x^2 + 24x = x^3/3 + 2x^2 + 8x

Rearranging the terms:

9x^2 + 24x = x^3/3 + 2x^2 + 8x

Multiplying through by 3 to clear the fraction:

27x^2 + 72x = x^3 + 6x^2 + 24x

Subtracting 27x^2 and 72x from both sides:

0 = x^3 - 21x^2

This equation doesn't have a valid solution, as x can be anything and still not satisfy the equation.