Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\left( {\dfrac{{2\sqrt {xy} }}{{x - y}} + \dfrac{{\sqrt x - \sqrt y }}{{2\left( {\sqrt x + \sqrt y } \right)}}} \right).\dfrac{{2\sqrt x }}{{\sqrt x + \sqrt y }} + \dfrac{y}{{\sqrt y - \sqrt x }}\\
= \left( {\dfrac{{2\sqrt {xy} }}{{\left( {\sqrt x - \sqrt y } \right)\left( {\sqrt x + \sqrt y } \right)}} + \dfrac{{\sqrt x - \sqrt y }}{{2\left( {\sqrt x + \sqrt y } \right)}}} \right).\dfrac{{2\sqrt x }}{{\sqrt x + \sqrt y }} + \dfrac{y}{{\sqrt y - \sqrt x }}\\
= \dfrac{{4.\sqrt {xy} + {{\left( {\sqrt x - \sqrt y } \right)}^2}}}{{2.\left( {\sqrt x - \sqrt y } \right)\left( {\sqrt x + \sqrt y } \right)}}.\dfrac{{2\sqrt x }}{{\sqrt x + \sqrt y }} + \dfrac{y}{{\sqrt y - \sqrt x }}\\
= \dfrac{{4\sqrt {xy} + x - 2\sqrt {xy} + y}}{{2.\left( {\sqrt x - \sqrt y } \right).\left( {\sqrt x + \sqrt y } \right)}}.\dfrac{{2\sqrt x }}{{\sqrt x + \sqrt y }} + \dfrac{y}{{\sqrt y - \sqrt x }}\\
= \dfrac{{x + 2\sqrt {xy} + y}}{{2\left( {\sqrt x - \sqrt y } \right).\left( {\sqrt x + \sqrt y } \right)}}.\dfrac{{2\sqrt x }}{{\sqrt x + \sqrt y }} + \dfrac{y}{{\sqrt y - \sqrt x }}\\
= \dfrac{{{{\left( {\sqrt x + \sqrt y } \right)}^2}}}{{2.\left( {\sqrt x - \sqrt y } \right).\left( {\sqrt x + \sqrt y } \right)}}.\dfrac{{2\sqrt x }}{{\sqrt x + \sqrt y }} + \dfrac{y}{{\sqrt y - \sqrt x }}\\
= \dfrac{{\sqrt x }}{{\sqrt x - \sqrt y }} + \dfrac{y}{{\sqrt y - \sqrt x }}\\
= \dfrac{{\sqrt x - y}}{{\sqrt x - \sqrt y }}
\end{array}\)
Em xem lại đề bài nhé, kia là \(\sqrt y \), không phải là \(y\)
