Question

Tính \(\frac{{\sqrt 3  + \sqrt 2 }}{{\sqrt 3  - \sqrt 2 }} - \frac{{\sqrt 3  - \sqrt 2 }}{{\sqrt 3  + \sqrt 2 }}\).

Answer 1

\(\frac{{\sqrt 3  + \sqrt 2 }}{{\sqrt 3  - \sqrt 2 }} - \frac{{\sqrt 3  - \sqrt 2 }}{{\sqrt 3  + \sqrt 2 }} = \frac{{{{\left( {\sqrt 3  + \sqrt 2 } \right)}^2} - {{\left( {\sqrt 3  - \sqrt 2 } \right)}^2}}}{{{{\left( {\sqrt 3 } \right)}^2} - {{\left( {\sqrt 2 } \right)}^2}}}\)

\( = \frac{{\left( {\sqrt 3  + \sqrt 2  + \sqrt 3  - \sqrt 2 } \right)\left( {\sqrt 3  + \sqrt 2  - \sqrt 3  + \sqrt 2 } \right)}}{{3 - 2}}\)

 \(\begin{array}{l} = 2\sqrt 3 .2\sqrt 2 \\ = 4\sqrt 6 \end{array}\)