$\displaystyle \frac{x^2-x+1}{x^2-x}$\displaystyle \frac{x^2-x+1}{x^2-x}

$\displaystyle \frac{x^2-x-1}{x^2-x}$\displaystyle \frac{x^2-x-1}{x^2-x}

$\displaystyle \frac{x-1}{x^2-x}$\displaystyle \frac{x-1}{x^2-x}

$\displaystyle \frac{x^2-x-1}{x-1}$\displaystyle \frac{x^2-x-1}{x-1}