[tex]\displaystyle\bf\\\frac{x^{2}-2x+1 }{4} \cdot\Big(\frac{2x}{x^{3} +1} :\frac{1-x}{x^{2} -x+1} +\frac{2}{x-1} \Big):\frac{x-1}{x+1} =\\\\\\=\frac{(x-1)^{2} }{4} \cdot\Big(\frac{2x}{(x+1)(x^{2} -x+1)} \cdot\frac{x^{2} -x+1}{1-x} +\frac{2}{x-1} \Big):\frac{x-1}{x+1} =\\\\\\=\frac{(x-1)^{2} }{4} \cdot\Big(\frac{2x}{(x+1)(1-x)} -\frac{2}{1-x} \Big):\frac{x-1}{x+1} =\\\\\\=\frac{(x-1)^{2} }{4} \cdot\frac{2x-2x-2}{(x+1)(1-x)} \cdot\frac{x+1}{x-1} =[/tex]

[tex]\displaystyle\bf\\=\frac{(x-1)^{2} }{4} \cdot\frac{2}{(x+1)(x-1)}\cdot\frac{x+1}{x-1} =\frac{1}{2}[/tex]