What is [(x+1)/(3x^(2)-3)] - [1/(3x+1)] in its simplest form?

First simplify the expression; 3x^(2)-3 to get;

[(x+1)/3(x^(2)-1)] - [1/(3x+1)] 

Using the fact that x^(2)-1 is the difference of two squares, we can simplify it to;

[(x+1)/3(x+1)(x-1)] - [1/(3x+1)] 

which simplifies to;

[1/3(x-1)] - [1/(3x+1)] 

finally adding the two gives

 4/3(x-1)(3x+1)