[tex]( \frac{3}{2(x-1)} - \frac{1}{2(x+1)} - \frac{4}{x^2-1}) : \frac{x-2}{x^2-2x+1} [/tex]
[tex] \frac{( \frac{3}{2(x-1)} - \frac{1}{2(x+1)} - \frac{4}{(x-1)(x+1)})(x^2-2x+1)}{x-2}[/tex]
[tex]\frac{(\frac{3(x+1)}{2(x+1)(x-1)} - \frac{x-1}{2(x+1)(x-1)} - \frac{8}{2(x+1)(x-1) })(x^2-2x+1)}{x-2}[/tex]
[tex] \frac{\frac{2(x-2)}{2(x+1)(x-1)}*(x^2-2x+1)}{x-2}[/tex]
[tex] \frac{\frac{x-2}{(x+1)(x-1)} *(x^2-2x+1)}{x-2}[/tex]
[tex] \frac{\frac{(x-2)(x-1)}{x+1}}{x-2}[/tex]
[tex] \frac{(x-2)(x-1)}{(x+1)(x-2)} = \frac{x-1}{x+1} [/tex]
