[tex]( \sqrt{ \frac{2}{3} } + \sqrt{ \frac{3}{2} } + \sqrt{ \frac{1}{6} } ) \div \sqrt{6} = [/tex]
[tex] \sqrt{ \frac{2}{3} } \div \sqrt{6} + \sqrt{ \frac{3}{2} } \div \sqrt{6} + \sqrt{ \frac{1}{6} } \div \sqrt{6} = [/tex]
[tex] \frac{ \sqrt{2} }{ \sqrt{3} } \times \frac{1}{ \sqrt{6}} + \frac{ \sqrt{3} }{ \sqrt{2} } \times \frac{ 1 }{ \sqrt{6 }} + \frac{ \sqrt{1} }{ \sqrt{6} } \times \frac{1}{ \sqrt{6}} = [/tex]
[tex]\frac{ 1 }{ \sqrt{3} } \times \frac{1}{ \sqrt{3}} + \frac{ 1 }{ \sqrt{2} } \times \frac{ 1 }{ \sqrt{2 }} + \frac{ 1 }{ \sqrt{6} } \times \frac{1}{ \sqrt{6}} = [/tex]
[tex] \frac{1}{3} + \frac{1}{2} + \frac{1}{6} [/tex]
[tex] \frac{2}{6} + \frac{3}{6} + \frac{1}{6} = \frac{6}{6} = 1[/tex]
