To add the fractions on the right side, first, find a common denominator. In this case, the least common multiple (LCM) of 3, 9, and 6 is 18.

2x + 4/x3 = (2x + 4) 6x / 6x3
5x - 2/9 = (5x - 2) 2x / 2x3
3x - 7/6 = (3x - 7) * 3 / 3x

Now, rewrite the equation with the common denominator:

(6(2x + 4) + 2(5x - 2) + 3(3x - 7))/18 = (6x(2x + 4) + 2x(5x - 2) + 3x(3x - 7))/18

Simplify the numerator:

(12x + 24 + 10x - 4 + 9x - 21)/18 = (12x^2 + 24x + 10x^2 - 4x + 9x^2 - 21x)/18

Combine like terms:

(31x - 1)/18 = (31x^2 + 24x)/18

Divide each term by 18:

31x/18 - 1/18 = 31x^2/18 + 24x/18

Simplify:

31x/18 - 1/18 = 31x^2/18 + 4x/3

Therefore, the solution to the equation is:

31x/18 - 1/18 = 31x^2/18 + 4x/3