I took your equation to mean: (2/(2x^2+5x-3))+(3/(2x+6))=(1/(4x-2))
Solve for x over the real numbers:
3/(2 x + 6) + 2/(2 x^2 + 5 x - 3) = 1/(4 x - 2)
Multiply both sides by (4 x - 2) (x + 3):
4 + 3 (2 x - 1) = x + 3
Expand out terms of the left hand side:
6 x + 1 = x + 3
Subtract x + 1 from both sides:
5 x = 2
Divide both sides by 5:
Answer: |x = 2/5
