Rút gọn biểu thức: A = \(\frac{{2{x^3} - 3{x^2} + 3x - 1}}{{{x^2} - x + 1}}\).

Ta có:

A = \(\frac{{2{x^3} - 3{x^2} + 3x - 1}}{{{x^2} - x + 1}} = \frac{{2{x^3} - {x^2} - 2{x^2} + x + 2x - 1}}{{{x^2} - x + 1}}\)

\( = \frac{{{x^2}\left( {2x - 1} \right) - x\left( {2x - 1} \right) + \left( {2x - 1} \right)}}{{{x^2} - x + 1}}\)

= \(\frac{{\left( {2x - 1} \right)\left( {{x^2} - x + 1} \right)}}{{{x^2} - x + 1}} = 2x - 1\).