How to show that (x-2)/(x^2-x+1)= ((2x-1)/(2(x^2-x+1)))-3/(2(x^2-x+1))?
$\displaystyle \displaystyle \begin{align*} \frac{2x - 1}{2\left(x^2 - x + 1\right)} - \frac{3}{2\left(x^2 - x + 1\right)} &\equiv \frac{2x - 1 - 3}{2\left(x^2 - x + 1\right)} \\ &\equiv \frac{2x - 4}{2\left(x^2 - x + 1\right)} \\ &\equiv \frac{2(x - 2)}{2\left(x^2 - x + 1\right)} \\ &\equiv \frac{x - 2}{x^2 - x + 1} \end{align*}$