Đáp án:
$\begin{array}{l}
Dkxd:x \ne y;x \ne - y\\
A = \left( {x - \dfrac{{4xy}}{{x + y}} + y} \right):\left( {\dfrac{x}{{x + y}} + \dfrac{y}{{y - x}} + \dfrac{{2xy}}{{{x^2} - {y^2}}}} \right)\\
= \left( {\dfrac{{\left( {x + y} \right)\left( {x + y} \right) - 4xy}}{{x + y}}} \right)\\
:\left( {\dfrac{x}{{x + y}} - \dfrac{y}{{x - y}} + \dfrac{{2xy}}{{\left( {x + y} \right)\left( {x - y} \right)}}} \right)\\
= \dfrac{{{x^2} + 2xy + {y^2} - 4xy}}{{x + y}}\\
:\dfrac{{x\left( {x - y} \right) - y\left( {x + y} \right) + 2xy}}{{\left( {x + y} \right)\left( {x - y} \right)}}\\
= \dfrac{{{x^2} - 2xy + {y^2}}}{{x + y}}.\dfrac{{\left( {x + y} \right)\left( {x - y} \right)}}{{{x^2} - xy - xy - {y^2} + 2xy}}\\
= \dfrac{{{{\left( {x - y} \right)}^2}}}{1}.\dfrac{{x - y}}{{{x^2} - {y^2}}}\\
= \dfrac{{{{\left( {x - y} \right)}^2}}}{{x + y}}
\end{array}$
