Simplify:3√2/√3 + √6 - 4√3/√6+√2 + √6/√2 + √3\(\

1.	Simplify:3√2/√3 + √6 - 4√3/√6+√2 + √6/√2 + √3\(\frac {3\sqrt2}{\sqrt3+\sqrt6} - \frac {4\sqrt3}{\sqrt6+\sqrt2} + \frac {\sqrt6}{\sqrt2+\sqrt3} \)
Answer» \(\frac {3\sqrt2}{\sqrt3+\sqrt6} - \frac {4\sqrt3}{\sqrt6+\sqrt2} + \frac {\sqrt6}{\sqrt2+\sqrt3} \) = \(\frac {3\sqrt2(\sqrt3 -\sqrt6)}{(\sqrt3+\sqrt6)(\sqrt3-\sqrt6)} -\frac {4\sqrt3(\sqrt6 -\sqrt2)}{(\sqrt6+\sqrt2)(\sqrt6-\sqrt2)} +\frac {\sqrt6(\sqrt2 -\sqrt3)}{(\sqrt2+\sqrt3)(\sqrt2-\sqrt3)}\) = \(\frac {3\sqrt6 - 6\sqrt3}{3-6} -\frac {12\sqrt2 - 4\sqrt6}{6-2} +\frac {2\sqrt3 - 3\sqrt2}{2-3} \) = \(\frac {3\sqrt6 + 6\sqrt3}{3} +\frac {4\sqrt6 - 12\sqrt2}{4} +\frac {3\sqrt2 - 2\sqrt3}{1} \) = \(\frac {-12\sqrt6 + 24\sqrt3 + 12\sqrt6 - 36\sqrt2 + 36\sqrt2 - 24\sqrt3}{12} = \frac 0{12} =0\)

Simplify:3√2/√3 + √6 - 4√3/√6+√2 + √6/√2 + √3\(\frac {3\sqrt2}{\sqrt3+\sqrt6} - \frac {4\sqrt3}{\sqrt6+\sqrt2} + \frac {\sqrt6}{\sqrt2+\sqrt3} \)

Answer»

\(\frac {3\sqrt2}{\sqrt3+\sqrt6} - \frac {4\sqrt3}{\sqrt6+\sqrt2} + \frac {\sqrt6}{\sqrt2+\sqrt3} \)

= \(\frac {3\sqrt2(\sqrt3 -\sqrt6)}{(\sqrt3+\sqrt6)(\sqrt3-\sqrt6)} -\frac {4\sqrt3(\sqrt6 -\sqrt2)}{(\sqrt6+\sqrt2)(\sqrt6-\sqrt2)} +\frac {\sqrt6(\sqrt2 -\sqrt3)}{(\sqrt2+\sqrt3)(\sqrt2-\sqrt3)}\)

= \(\frac {3\sqrt6 - 6\sqrt3}{3-6} -\frac {12\sqrt2 - 4\sqrt6}{6-2} +\frac {2\sqrt3 - 3\sqrt2}{2-3} \)

= \(\frac {3\sqrt6 + 6\sqrt3}{3} +\frac {4\sqrt6 - 12\sqrt2}{4} +\frac {3\sqrt2 - 2\sqrt3}{1} \)

= \(\frac {-12\sqrt6 + 24\sqrt3 + 12\sqrt6 - 36\sqrt2 + 36\sqrt2 - 24\sqrt3}{12} = \frac 0{12} =0\)

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