Tính: ​\( \frac{3}{{\sqrt 7 - 1}} - \frac{{\sqrt 7 - \sqrt {21} }}{{2 - 2\sqrt 3 }}\)

* Hướng dẫn giải

Ta có:

 \(\begin{array}{*{20}{l}} {\frac{3}{{\sqrt 7 - 1}} - \frac{{\sqrt 7 - \sqrt {21} }}{{2 - 2\sqrt 3 }} = \frac{{3.\left( {\sqrt 7 + 1} \right)}}{{\left( {\sqrt 7 - 1} \right).\left( {\sqrt 7 + 1} \right)}} - \frac{{\sqrt 7 - \sqrt 7 .\sqrt 3 }}{{2.\left( {1 - \sqrt 3 } \right)}}}\\ { = \frac{{3\left( {\sqrt 7 + 1} \right)}}{{{{\left( {\sqrt 7 } \right)}^2} - 1}} - \frac{{\sqrt 7 \left( {1 - \sqrt 3 } \right)}}{{2\left( {1 - \sqrt 3 } \right)}}}\\ { = \frac{{3\left( {\sqrt 7 + 1} \right)}}{6} - \frac{{\sqrt 7 }}{2} = \frac{{\sqrt 7 + 1}}{2} - \frac{{\sqrt 7 }}{2} = \frac{1}{2}} \end{array}\)