[tex]\frac{x}{x + 1} - \frac{1}{x - 1} + \frac{2x}{x^{2} - 1}[/tex]
[tex]\frac{x}{x + 1} - \frac{1}{x - 1} + \frac{2x}{(x + 1)(x - 1)}[/tex]
[tex]\frac{x(x - 1)}{(x + 1)(x - 1)} - \frac{1(x + 1)}{(x + 1)(x - 1)} + \frac{2x}{(x + 1)(x - 1)}[/tex]
[tex]\frac{x^{2} - x}{(x + 1)(x - 1)} - \frac{x + 1}{(x + 1)(x - 1)} + \frac{2x}{(x + 1)(x - 1)}[/tex]
[tex]\frac{x^{2} - x + x + 1 + 2x}{(x + 1)(x - 1)}[/tex]
[tex]\frac{x^{2} + 2x + 1}{(x + 1)(x - 1)}[/tex]
[tex]\frac{(x + 1)(x + 1)}{(x + 1)(x - 1)}[/tex]
[tex]\frac{(x + 1)^{2}}{(x + 1)(x - 1)}[/tex]
[tex]\frac{x + 1}{x - 1}[/tex]
