To solve this equation, first find a common denominator for the fractions:

Common denominator is (3x^2-x+2)(3x^2+5x+2)

Rewrite the equation with common denominator:

(2x(3x^2+5x+2) - 7x(3x^2-x+2)) / ((3x^2-x+2)(3x^2+5x+2)) = 1

Expanding both numerator terms:

(6x^3 + 10x^2 + 4x - 21x^3 + 7x^2 - 14x) / ((3x^2-x+2)(3x^2+5x+2)) = 1

Simplify the numerator:

(-15x^3 + 17x^2 - 10x) / ((3x^2-x+2)(3x^2+5x+2)) = 1

Now set the equation to equal 1, as the new equation is already in its simplest form:

-15x^3 + 17x^2 - 10x = (3x^2-x+2)(3x^2+5x+2)

Expanding the right side:

-15x^3 + 17x^2 - 10x = 9x^4 + 15x^3 + 6x^2 - 3x^3 - 5x^2 - 2x + 18x^2 + 30x + 12

Rearranging terms:

-15x^3 + 17x^2 - 10x = 9x^4 + 12x^3 + 19x^2 + 28x + 12

Set on side equal to zero by moving everything to the left side:

9x^4 + 12x^3 + 19x^2 + 28x + 12 + 15x^3 - 17x^2 + 10x = 0

Combine like terms:

9x^4 + 27x^3 + 2x^2 + 38x + 12 = 0

This is a fourth-degree polynomial equation that can be solved by factoring, numerical methods, or other techniques.