\(C=\left(\frac{1}{x-1}-\frac{2x}{x^3+x-x^2-1}\right):\left(1-\frac{2x}{x^2+1}\right)\)
\(C=\left(\frac{1}{x-1}-\frac{2x}{x^2\left(x-1\right)+x-1}\right):\left(\frac{x^2+1-2x}{x^2+1}\right)\)
\(C=\left(\frac{1}{x-1}-\frac{2x}{\left(x-1\right)\left(x^2+1\right)}\right):\left[\frac{\left(x-1\right)^2}{x^2+1}\right]\)
\(C=\frac{x^2+1-2x}{\left(x-1\right)\left(x^2+1\right)}.\frac{x^2+1}{\left(x-1\right)^2}\)
\(C=\frac{1}{x-1}\)