Question

 \dfrac{ 6  }{  \sqrt{ 3  }  -3  }  - \dfrac{ 3+ \sqrt{ 3  }    }{  \sqrt{ 3  }  +1  }  + \sqrt{  (   \sqrt{ 3-2  }   )   ^{2}    }   

Answer 1

\( \dfrac{ 6 }{ \sqrt{ 3 } -3 } - \dfrac{ 3+ \sqrt{ 3 } }{ \sqrt{ 3 } +1 } + \sqrt{ ( \sqrt{ 3-2 } ) ^{2} } \)

\(=\dfrac{\sqrt{36}}{\sqrt{3}\left(\sqrt{3}-1\right)}-\dfrac{\sqrt{3}\left(\sqrt{3}+1\right)}{\sqrt{3}+1}+1\)

\(=\dfrac{\sqrt{12}}{\sqrt{3}-1}-\sqrt{3}+1\)

\(=\dfrac{\sqrt{12}\left(\sqrt{3}+1\right)}{\sqrt{4}}-\sqrt{3}+1\)

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

\(=3+\sqrt{3}-\sqrt{3}+1\)

\(=4\)