Rút gọn: \( {\frac{{\left( {x\sqrt y + y\sqrt x } \right)\left( {\sqrt x - \sqrt y } \right)}}{{\sqrt {xy} }}}\)

* Hướng dẫn giải

 \(\begin{array}{*{20}{l}} {\frac{{\left( {x\sqrt y + y\sqrt x } \right)\left( {\sqrt x - \sqrt y } \right)}}{{\sqrt {xy} }}}\\ { = \frac{{\left( {\sqrt x .\sqrt x .\sqrt y + \sqrt y .\sqrt y .\sqrt x } \right)\left( {\sqrt x - \sqrt y } \right)}}{{\sqrt {xy} }}}\\ { = \frac{{\sqrt {xy} \left( {\sqrt x + \sqrt y } \right)\left( {\sqrt x - \sqrt y } \right)}}{{\sqrt {xy} }}}\\ { = \left( {\sqrt x + \sqrt y } \right)\left( {\sqrt x - \sqrt y } \right)}\\ { = {{\left( {\sqrt x } \right)}^2} - {{\left( {\sqrt y } \right)}^2}}\\ { = x - y.} \end{array}\)