[tex] \sqrt{3} + \sqrt{6} ( \frac{1}{ \sqrt{3} } + \frac{1}{ \sqrt{2} } )-4 \sqrt{6} ( \frac{1}{ \sqrt{8} } - \frac{1}{ \sqrt{12} } )-3 \sqrt{2} =[/tex]
[tex] \sqrt{3} + \sqrt{6} ( \frac{ \sqrt{3} }{3} + \frac{ \sqrt{2} }{2} )-4 \sqrt{6} ( \frac{ \sqrt{2} }{4} - \frac{ \sqrt{3} }{6} )-3 \sqrt{2} =[/tex]
[tex] \sqrt{3} + \sqrt{6} ( \frac{2 \sqrt{3} +3 \sqrt{2} }{6} )-4 \sqrt{6} ( \frac{3 \sqrt{2}-2 \sqrt{3} }{12} )-3 \sqrt{2} [/tex]
[tex] \sqrt{3} + \frac{6 \sqrt{2} +6 \sqrt{3} }{6} - \frac{6 \sqrt{3} +6 \sqrt{2} }{3} -3 \sqrt{2} =[/tex]
[tex] \sqrt{3} + \frac{6( \sqrt{2}+ \sqrt{3} ) }{6} - \frac{3(2 \sqrt{3} +2 \sqrt{2}) }{3} -3 \sqrt{2} =[/tex]
[tex] \sqrt{3} + \sqrt{2} + \sqrt{3} -2 \sqrt{3} +2 \sqrt{2} -3 \sqrt{2} =0[/tex]
