Tính \(\begin{array}{l} \frac{2}{{\sqrt 6 - 2}} + \frac{2}{{\sqrt 6 + 2}} + \frac{5}{{\sqrt 6 }} \end{array}\) là:

* Hướng dẫn giải

 \(\begin{array}{l} \frac{2}{{\sqrt 6 - 2}} + \frac{2}{{\sqrt 6 + 2}} + \frac{5}{{\sqrt 6 }} = \frac{{2\left( {\sqrt 6 + 2} \right)}}{{6 - 4}} + \frac{{2\left( {\sqrt 6 - 2} \right)}}{{6 - 4}} + \frac{{5\sqrt 6 }}{6}\\ = \frac{{2\sqrt 6 + 4 + 2\sqrt 6 - 4}}{2} + \frac{{5\sqrt 6 }}{6}\\ = \frac{{4\sqrt 6 }}{2} + \frac{{5\sqrt 6 }}{6}\\ = \frac{{17\sqrt 6 }}{6} \end{array}\)