Hãy rút gọn: \(\dfrac{{a\sqrt b + b\sqrt a }}{{\sqrt {ab} }}:\dfrac{1}{{\sqrt a - \sqrt b }} \).

* Hướng dẫn giải

 \(\dfrac{{a\sqrt b + b\sqrt a }}{{\sqrt {ab} }}:\dfrac{1}{{\sqrt a - \sqrt b }}\)

\(=\dfrac{{\sqrt a \sqrt a \sqrt b + \sqrt b \sqrt b \sqrt a }}{{\sqrt {ab} }}:\dfrac{1}{{\sqrt a - \sqrt b }}\)

\(= \left( {\sqrt a + \sqrt b } \right)\left( {\sqrt a - \sqrt b } \right)\)

\(= {\left( {\sqrt a } \right)^2} - {\left( {\sqrt b } \right)^2} = a - b.\)