[tex]( \frac{6}{2 \sqrt{3} } - \sqrt{6} )+( \frac{6}{ \sqrt{3} } + \sqrt{2} )-( \frac{4 \sqrt{3} }{\sqrt{6} } - \sqrt{2} )\\ \\ =( \frac{3}{ \sqrt{3} } - \sqrt{6} )+( \frac{2 \times 3}{ \sqrt{3} } + \sqrt{2} )-( \frac{2 \sqrt{4 \times 3} }{\sqrt{6} } - \sqrt{2} )\\ \\ =( \frac{ \sqrt{3} \times \sqrt{3} }{\sqrt{3} } - \sqrt{6} )+( \frac{2 \times \sqrt{3} \times \sqrt{3}}{ \sqrt{3} } + \sqrt{2} )-( \frac{2 \times \sqrt{2} \times \sqrt{2} \times \sqrt{3} }{\sqrt{2} \times \sqrt{3} } - \sqrt{2} )[/tex]
[tex]=( \sqrt{3} } - \sqrt{6} )+( 2 \sqrt{3} + \sqrt{2} )-( 2 \sqrt{2}- \sqrt{2} )\\ \\= \sqrt{3} } - \sqrt{6}+ 2 \sqrt{3} + \sqrt{2} - 2 \sqrt{2}+ \sqrt{2}\\ \\=3 \sqrt{3}+ 2\sqrt{2}-2 \sqrt{2}- \sqrt{6}\\ \\ = 3 \sqrt{3}- \sqrt{6}[/tex]
