Thu gọn biểu thức: \(\frac{{x{}^6 - {y^6}}}{{{x^4} - {y^4} - {x^3}y + x{y^3}}}\).

Ta có: \(\frac{{{x^6} - {y^6}}}{{{x^4} - {y^4} - {x^3}y + x{y^3}}}\)

\( = \frac{{{{\left( {{x^2}} \right)}^3} - {{\left( {{y^2}} \right)}^3}}}{{\left( {{x^4} - {y^4}} \right) - \left( {{x^3}y - x{y^3}} \right)}}\)\( = \frac{{\left( {{x^3} - {y^3}} \right)\left( {{x^3} + {y^3}} \right)}}{{{x^3}\left( {x - y} \right) + {y^3}\left( {x - y} \right)}}\)

\( = \frac{{\left( {x - y} \right)\left( {{x^2} + xy + {y^2}} \right)\left( {{x^3} + {y^3}} \right)}}{{\left( {x - y} \right)\left( {{x^3} + {y^3}} \right)}}\)\( = {x^2} + xy + {y^2}\).