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\displaystyle[br]\begin{equation*}\frac{\sqrt{3} + \sqrt{2} - 1}{\sqrt{3} - \sqrt{6} + 1} = 2 + a\sqrt{2} + b\sqrt{3} + c\sqrt{6}\end{equation*}
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\displaystyle[br]\begin{equation*}\frac{\sqrt{3} + \sqrt{2} - 1}{1 + \sqrt{3} - \sqrt{6}} \times \frac{1 + \sqrt{3} + \sqrt{6}}{1 + \sqrt{3} + \sqrt{6}} = \frac{1 + 2\sqrt{2} + \sqrt{3}}{\sqrt{3} - 1} \times \frac{\sqrt{3} + 1}{\sqrt{3}+1} = 2 + \sqrt{2} + \sqrt{3} + \sqrt{6}\end{equation*}
\displaystyle[br]\begin{equation*}\frac{\sqrt{3} + \sqrt{2} - 1}{1 + \sqrt{3} - \sqrt{6}} \times \frac{1 + \sqrt{3} + \sqrt{6}}{1 + \sqrt{3} + \sqrt{6}} = \frac{1 + 2\sqrt{2} + \sqrt{3}}{\sqrt{3} - 1} \times \frac{\sqrt{3} + 1}{\sqrt{3}+1} = 2 + \sqrt{2} + \sqrt{3} + \sqrt{6}\end{equation*}
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