$\dfrac{x+1}{x-1} - \dfrac{x-1}{x+1} + \dfrac{x^{2} - 4x -1}{x^{2}-1}$
= $\dfrac{(x+1)^{2}}{x^{2}-1} - \dfrac{(x-1)^{2}}{x^{2}-1} + \dfrac{x^{2} - 4x -1}{x^{2}-1}$
= $\dfrac{(x+1+x-1)(x+1-x+1) + x^{2} - 4x - 1}{x^{2}-1}$
= $\dfrac{4x + x^{2} -4x-1}{x^{2}-1}$
= $\dfrac{x^{2} - 1}{x^{2}-1}$
= $1$