[tex] \frac{ \sqrt{3} }{ \sqrt{2} } + \frac{3 \sqrt{6} }{2} - \sqrt{24} [/tex]
[tex] = \frac{ \sqrt{3} \times \sqrt{2} }{ {( \sqrt{2} )}^{2} } + \frac{3 \sqrt{6} }{2} - 2 \sqrt{6} [/tex]
[tex] = \frac{ \sqrt{3 \times 2} }{2} + \frac{3 \sqrt{6} }{2} - 2 \sqrt{6} [/tex]
[tex] = \frac{ \sqrt{6} }{2} + \frac{ 3\sqrt{6} }{2} - 2 \sqrt{6} [/tex]
[tex] = \frac{ \sqrt{6} + 3 \sqrt{6} }{2} - 2\sqrt{6} [/tex]
[tex] = \frac{4 \sqrt{6} }{2} - 2 \sqrt{6} [/tex]
[tex] = 2 \sqrt{6} - 2 \sqrt{6} [/tex]
[tex] = 0[/tex]
