To solve the given equation, let's first simplify the expression on both sides:

7x^2 + 3/x^2 - 9 = 3x - 2/x + 3 + 4x - 3/x - 3

To simplify the equation, multiply each side by x^2 to get rid of the fractions:

7x^4 + 3 - 9x^2 = 3x^3 - 2x + 3x^2 + 4x^3 - 3x - 3x^2

Now, combine like terms:

7x^4 - 9x^2 + 3 = 7x^3 - 5x

Rearranging the terms:

7x^4 - 7x^3 - 9x^2 + 5x + 3 = 0

This is the simplified form of the given equation.