[tex]\displaystyle E(x)=\left(x-\frac1{1-x}\right):\frac{x^2-x+1}{x^2-2x+1}=\frac{x(1-x)-1}{1-x}\cdot\frac{x^2-2x+1}{x^2-x+1}=\frac{x-x^2-1}{-(x-1)}\cdot\frac{(x-1)^2}{x^2-x+1}=-(-x^2+x-1)\cdot\frac{x-1}{x^2-x+1}=(x^2-x+1)\cdot\frac{x-1}{x^2-x+1}=x-1[/tex]
