[tex] \frac{x+3}{3x-2} - \frac{x-3}{3x+2} = \frac{44}{9x^2-4}[/tex]
[tex] \frac{(x+3)(3x+2) - (x-3)(3x-2)}{(3x-2)(3x+2)} = \frac{44}{(3x+2)(3x-2)}[/tex]
[tex] (x+3)(3x+2) - (x-3)(3x-2) = 44[/tex]
[tex] (3x^2 + 11x + 6) - (3x^2 - 11x + 6) = 44[/tex]
[tex] 22x = 44[/tex]
[tex] x = 2[/tex]Substituting x = 2 into the original does not give any extraneous solutions, so this is the answer.
