Explicație pas cu pas:
[tex]E(x) = (x - \frac{1}{1-x}) : \frac{x^2 - x + 1}{x^2 - 2x +1}\\\\E(x) = (\frac{x(1-x)}{1-x}- \frac{1}{1-x}) * \frac{x^2 - 2x +1}{x^2 - x + 1}\\\\E(x) = \frac{x-x^2-1}{1-x} * \frac{(x-1)^2}{x^2 - x + 1}\\\\E(x) = \frac{x-x^2-1}{(-1)*(x-1)} * \frac{(x-1)^2}{x^2 - x + 1}\\\\E(x) = \frac{(-1)*(x^2-x+1)}{(-1)} * \frac{(x-1)}{x^2 - x + 1}\\\\E(x) = \frac{-1}{-1} * (x-1)\\\\E(x) = x-1[/tex]
