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\(=\cfrac{\sqrt2[(2+\sqrt3)(\sqrt3-1)-(2-\sqrt3)(\sqrt3+1)]}{\sqrt3(\sqrt3+1)(\sqrt3-1)}\)
\(=\cfrac{\sqrt2[(2\sqrt3-2+3-\sqrt3)-(2\sqrt3+2-3-\sqrt3)]}{\sqrt3(3-1)}\)
\(=\cfrac{\sqrt2[(\sqrt3+1)-(\sqrt3-1)]}{2\sqrt3}\)
\(=\cfrac{\sqrt2[\sqrt3+1-\sqrt3+1]}{2\sqrt3}\)
\(=\cfrac{2\sqrt2}{2\sqrt3}\)
\(=\cfrac{\sqrt2}{\sqrt3}\)
\(=\cfrac{\sqrt6}{3}\)