Đáp án: 0
Giải thích các bước giải:
$\begin{array}{l}
A = \left( {\dfrac{1}{{1 + \sqrt {7 - \sqrt {24} } }} - \dfrac{1}{{\sqrt {7 + \sqrt {24} - 1} }}} \right):\left( {\sqrt 7 - \sqrt 3 } \right)\\
= \left( {\dfrac{1}{{1 + \sqrt {7 - 2\sqrt 6 } }} - \dfrac{1}{{\sqrt {7 + 2\sqrt 6 } - 1}}} \right).\dfrac{1}{{\sqrt 7 - \sqrt 3 }}\\
= \left( {\dfrac{1}{{1 + \sqrt {{{\left( {\sqrt 6 - 1} \right)}^2}} }} - \dfrac{1}{{\sqrt {{{\left( {\sqrt 6 + 1} \right)}^2}} - 1}}} \right).\dfrac{1}{{\sqrt 7 - \sqrt 3 }}\\
= \left( {\dfrac{1}{{1 + \sqrt 6 - 1}} - \dfrac{1}{{\sqrt 6 + 1 - 1}}} \right).\dfrac{1}{{\sqrt 7 - \sqrt 3 }}\\
= \left( {\dfrac{1}{{\sqrt 6 }} - \dfrac{1}{{\sqrt 6 }}} \right).\dfrac{1}{{\sqrt 7 - \sqrt 3 }}\\
= 0
\end{array}$
