We have:

2x/(x + 3) + 1/(x - 1) = 4/x^2 + 2x - 3

To solve for x, we need to find a common denominator on the left side of the equation:

(2x(x - 1) + (x + 3))/(x^2 + 2x - 3) = 4/x^2 + 2x - 3

Expanding the left side:

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

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

Multiplying both sides by x^2 + 2x - 3 to clear the denominators:

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

2x^2 - x + 3 = 4 + 2x^3 + 4x^2 - 6x - 3x^2 - 6x + 9

2x^2 - x + 3 = 4 + x^3 + x^2 - 6x + 9

Combine like terms:

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

This is a cubic equation that may not have a simple solution. One approach to solve this equation is to use numerical methods such as graphing or software to find roots.