Hãy rút gọn biểu thức \(M = \left( {\dfrac{1}{{a - \sqrt a }} + \dfrac{1}{{\sqrt a - 1}}} \right):\dfrac{{\sqrt a + 1}}{{a - 2\sqrt a + 1}}\)&

* Hướng dẫn giải

 \(M = \left( {\dfrac{1}{{a - \sqrt a }} + \dfrac{1}{{\sqrt a - 1}}} \right):\dfrac{{\sqrt a + 1}}{{a - 2\sqrt a + 1}}\)

\(= \left[ {\dfrac{1}{{\sqrt a \left( {\sqrt a - 1} \right)}} + \dfrac{{\sqrt a }}{{\sqrt a \left( {\sqrt a - 1} \right)}}} \right]:\dfrac{{\sqrt a + 1}}{{a - 2\sqrt a + 1}}\)

\(= \dfrac{{1 + \sqrt a }}{{\sqrt a \left( {\sqrt a - 1} \right)}} \cdot \dfrac{{{{\left( {\sqrt a - 1} \right)}^2}}}{{\sqrt a + 1}}\)

\(= \dfrac{{\sqrt a - 1}}{{\sqrt a }} = 1 - \dfrac{1}{{\sqrt a }}\)