1/ 2 + căn 3 + căn 2/ căn 6 – 2/ 3 + căn 3

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1. Đáp án:

   $\begin{array}{l}
   \dfrac{1}{{2 + \sqrt 3 }} + \dfrac{{\sqrt 2 }}{{\sqrt 6 }} – \dfrac{2}{{3 + \sqrt 3 }}\\
    = \dfrac{{2 – \sqrt 3 }}{{\left( {2 + \sqrt 3 } \right)\left( {2 – \sqrt 3 } \right)}} + \dfrac{1}{{\sqrt 3 }} – \dfrac{{2\left( {3 – \sqrt 3 } \right)}}{{{3^2} – 3}}\\
    = \dfrac{{2 – \sqrt 3 }}{{4 – 3}} + \dfrac{{\sqrt 3 }}{3} – \dfrac{{2\left( {3 – \sqrt 3 } \right)}}{{9 – 3}}\\
    = 2 – \sqrt 3  + \dfrac{1}{3}.\sqrt 3  + \dfrac{1}{3}\left( {3 – \sqrt 3 } \right)\\
    = 2 – \dfrac{2}{3}.\sqrt 3  + 1 – \dfrac{1}{3}.\sqrt 3 \\
    = 3 – \sqrt 3 
   \end{array}$

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