To simplify the expression 2/(x-1) - x/(x^2+1) - 1/(x+1), we need to find a common denominator for all three terms.
The common denominator for the three terms is (x-1)(x^2+1)(x+1). We can rewrite each term using this denominator as follows:
2/(x-1) = 2*(x^2+1)*(x+1) / [(x-1)(x^2+1)(x+1)]
x/(x^2+1) = x*(x-1)*(x+1) / [(x-1)(x^2+1)(x+1)]
1/(x+1) = (x^2+1) / [(x-1)(x^2+1)(x+1)]
Now, we can combine the three terms by subtracting the second and third terms from the first, and simplify as follows:
2*(x^2+1)*(x+1) / [(x-1)(x^2+1)(x+1)] - x*(x-1)*(x+1) / [(x-1)(x^2+1)(x+1)] - (x^2+1) / [(x-1)(x^2+1)(x+1)]
= [2*(x^2+1)*(x+1) - x*(x-1)*(x+1) - (x^2+1)] / [(x-1)(x^2+1)(x+1)]
= [2x^3 + 2x - x^3 + x^2 - x^2 - 1] / [(x-1)(x^2+1)(x+1)]
= (x^3 + 2x - 1) / [(x-1)(x^2+1)(x+1)]
Therefore, the simplified expression is (x^3 + 2x - 1) / [(x-1)(x^2+1)(x+1)].