Tính giá trị biểu thức \( \left( {\frac{{\sqrt {14} - \sqrt 7 }}{{1 - \sqrt 2 }} + \frac{{\sqrt {15} - \sqrt 5 }}{{1 - \sqrt 3 }}} \right):\frac{1}{{\sqrt 7 - \sqrt 5 }}\)

* Hướng dẫn giải

 \(\begin{array}{l} \left( {\frac{{\sqrt {14} - \sqrt 7 }}{{1 - \sqrt 2 }} + \frac{{\sqrt {15} - \sqrt 5 }}{{1 - \sqrt 3 }}} \right):\frac{1}{{\sqrt 7 - \sqrt 5 }} = \left( {\frac{{\sqrt 2 .\sqrt 7 - \sqrt 7 }}{{1 - \sqrt 2 }} + \frac{{\sqrt 5 .\sqrt 3 - \sqrt 5 }}{{1 - \sqrt 3 }}} \right):\frac{1}{{\sqrt 7 - \sqrt 5 }}\\ = \left( {\frac{{\sqrt 7 \left( {\sqrt 2 - 1} \right)}}{{1 - \sqrt 2 }} + \frac{{\sqrt 5 \left( {\sqrt 3 - 1} \right)}}{{1 - \sqrt 3 }}} \right).\left( {\sqrt 7 - \sqrt 5 } \right)\\ = \left( { - \sqrt 7 - \sqrt 5 } \right).\left( {\sqrt 7 - \sqrt 5 } \right)\\ = - \left( {\sqrt 7 + \sqrt 5 } \right)\left( {\sqrt 7 - \sqrt 5 } \right) = - \left( {7 - 5} \right) = - 2 \end{array}\)