Đáp án:
\[6 - 2\sqrt 2 - \sqrt 3 \]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\dfrac{{3 - \sqrt 3 }}{{1 - \sqrt 3 }} + \dfrac{2}{{2\sqrt 3 + 3}} + \dfrac{4}{{\sqrt 2 }}\\
= \dfrac{{{{\sqrt 3 }^2} - \sqrt 3 }}{{1 - \sqrt 3 }} + \dfrac{{2.\left( {3 - 2\sqrt 2 } \right)}}{{\left( {3 + 2\sqrt 2 } \right)\left( {3 - 2\sqrt 2 } \right)}} + \dfrac{{2.2}}{{\sqrt 2 }}\\
= \dfrac{{\sqrt 3 \left( {\sqrt 3 - 1} \right)}}{{1 - \sqrt 3 }} + \dfrac{{2.\left( {3 - 2\sqrt 2 } \right)}}{{{3^2} - {{\left( {2\sqrt 2 } \right)}^2}}} + \dfrac{{2.{{\sqrt 2 }^2}}}{{\sqrt 2 }}\\
= - \sqrt 3 + \dfrac{{6 - 4\sqrt 2 }}{{9 - 8}} + 2\sqrt 2 \\
= - \sqrt 3 + \dfrac{{6 - 4\sqrt 2 }}{1} + 2\sqrt 2 \\
= - \sqrt 3 + 6 - 4\sqrt 2 + 2\sqrt 2 \\
= 6 - 2\sqrt 2 - \sqrt 3
\end{array}\)
