Đáp án:
\(\dfrac{{3\sqrt {xy} }}{{x - \sqrt {xy} + y}}\)
Giải thích các bước giải:
\(\begin{array}{l}
DK:x \ge 0;y \ge 0;x \ne y\\
H = \left[ {\dfrac{{\left( {\sqrt x - \sqrt y } \right)\left( {\sqrt x + \sqrt y } \right)}}{{\sqrt x - \sqrt y }} - \dfrac{{\left( {\sqrt x - \sqrt y } \right)\left( {x - \sqrt {xy} + y} \right)}}{{\left( {\sqrt x - \sqrt y } \right)\left( {\sqrt x + \sqrt y } \right)}}} \right]:\dfrac{{x - 2\sqrt {xy} + y + \sqrt {xy} }}{{\sqrt x + \sqrt y }}\\
= \left[ {\left( {\sqrt x + \sqrt y } \right) - \dfrac{{x - \sqrt {xy} + y}}{{\sqrt x + \sqrt y }}} \right].\dfrac{{\sqrt x + \sqrt y }}{{x - \sqrt {xy} + y}}\\
= \left[ {\dfrac{{x + 2\sqrt {xy} + y - x + \sqrt {xy} - y}}{{\sqrt x + \sqrt y }}} \right].\dfrac{{\sqrt x + \sqrt y }}{{x - \sqrt {xy} + y}}\\
= \dfrac{{3\sqrt {xy} }}{{x - \sqrt {xy} + y}}
\end{array}\)
