express $\displaystyle \frac{x+1}{3x^{2}-3} - \frac{1}{3x+1} $

as a single fraction in its simplest form.

I got $\displaystyle \frac{4x+4}{3x^{3} + 9x^{2} + 9x -3} $ but thats not the correct answer, can someone show me hot to get to $\displaystyle \frac{4}{3(x-1)(3x+1)} $

thank you.