Tính giá trị biểu thức 2 căn bậc hai 15 - 2 căn bậc hai 10 + căn bậc hai 6

\[\frac{{2\sqrt {15} - 2\sqrt {10} + \sqrt 6 - 3}}{{2\sqrt 5 - 2\sqrt {10} - \sqrt 3 + \sqrt 6 }}\]

\[ = \frac{{\left( {2\sqrt {15} - 2\sqrt {10} } \right) - \left( {3 - \sqrt 6 } \right)}}{{\left( {2\sqrt 5 - 2\sqrt {10} } \right) - \left( {\sqrt 3 - \sqrt 6 } \right)}}\]

\[ = \frac{{2\sqrt 5 \left( {\sqrt 3 - \sqrt 2 } \right) - \sqrt 3 \left( {\sqrt 3 - \sqrt 2 } \right)}}{{2\sqrt 5 \left( {1 - \sqrt 2 } \right) - \sqrt 3 \left( {1 - \sqrt 2 } \right)}}\]

\[ = \frac{{\left( {2\sqrt 5 - \sqrt 3 } \right)\left( {\sqrt 3 - \sqrt 2 } \right)}}{{\left( {2\sqrt 5 - \sqrt 3 } \right)\left( {1 - \sqrt 2 } \right)}}\]

\[ = \frac{{\sqrt 3 - \sqrt 2 }}{{1 - \sqrt 2 }}\]

\[ = \frac{{\left( {\sqrt 3 - \sqrt 2 } \right)\left( {1 + \sqrt 2 } \right)}}{{\left( {1 - \sqrt 2 } \right)\left( {1 + \sqrt 2 } \right)}}\]

\[ = \frac{{\left( {\sqrt 3 - \sqrt 2 } \right)\left( {1 + \sqrt 2 } \right)}}{{1 - 2}}\]

\[ = - \left( {\sqrt 3 - \sqrt 2 } \right)\left( {1 + \sqrt 2 } \right)\]

\[ = - \left( {\sqrt 3 + \sqrt 6 - \sqrt 2 - 2} \right)\]

\[ = - \sqrt 3 - \sqrt 6 + \sqrt 2 + 2\].