Đáp án:
$\begin{array}{l}
\frac{{{x^2} + xy}}{{{x^3} + {x^2}y + x{y^2} + {y^3}}}:\left( {\frac{1}{{x - y}} - \frac{{2xy}}{{{x^3} - {x^2}y + x{y^2} - {y^3}}}} \right)\\
= \frac{{x\left( {x + y} \right)}}{{{x^2}\left( {x + y} \right) + {y^2}\left( {x + y} \right)}}:\left( {\frac{1}{{x - y}} - \frac{{2xy}}{{\left( {x - y} \right)\left( {{x^2} + {y^2}} \right)}}} \right)\\
= \frac{{x\left( {x + y} \right)}}{{\left( {x + y} \right)\left( {{x^2} + {y^2}} \right)}}:\left( {\frac{{{x^2} + {y^2} - 2xy}}{{\left( {x - y} \right)\left( {{x^2} + {y^2}} \right)}}} \right)\\
= \frac{x}{{{x^2} + {y^2}}}.\frac{{\left( {x - y} \right)\left( {{x^2} + {y^2}} \right)}}{{{{\left( {x - y} \right)}^2}}}\\
= \frac{x}{{x - y}}
\end{array}$
