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\(\cfrac{4\sqrt{3}}{2-\sqrt{2}}-\cfrac{30}{4\sqrt{3}-\sqrt{18}}-\cfrac{\sqrt{18}}{3-\sqrt{12}}\)
\(=\cfrac{4\sqrt{3} (2+\sqrt{2}}{(2-\sqrt{2})(2+\sqrt{2})}\)

\( -\cfrac{30(4\sqrt{3}+\sqrt{18})}{(4\sqrt{3}-\sqrt{18})(4\sqrt{3}+\sqrt{18})}\)

\( -\cfrac{\sqrt{18} (3+\sqrt{12})}{(3-\sqrt{12})(3+\sqrt{12})} \)

\(=\cfrac{4\sqrt{3} (2+\sqrt{2})}{4-2}-\cfrac{30(4\sqrt{3}+\sqrt{3×3×2})}{48-18}\)

\(-\cfrac{\sqrt{3×3×2} (3+\sqrt{2×2×3})}{9-12}\)

\(=\cfrac{4\sqrt{3} (2+\sqrt{2})}{2}-\cfrac{30(4\sqrt{3}+3\sqrt{2})}{30}\)

\(-\cfrac{3\sqrt{2} (3+2\sqrt{3})}{-3}\)

\(=2\sqrt{3} (2+\sqrt{2})-(4\sqrt{3}+3\sqrt{2})\)

\(+\sqrt{2} (3+2\sqrt{3})\)

\(=4\sqrt{3}+2\sqrt{6}-4\sqrt{3}-3\sqrt{2}+3\sqrt{2}+2\sqrt{6}\)
\(=4\sqrt{6}\)