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\(\cfrac{4√3}{2-√2}-\cfrac{30}{4√3-√18}-\cfrac{√18}{3-√12}\)
\(=\cfrac{4\sqrt{3}(2+\sqrt{2})}{(2-\sqrt{2})(2+\sqrt{2})}\) \(-\cfrac{30(4\sqrt{3}+\sqrt{18})}{(4\sqrt{3}-\sqrt{18})(4\sqrt{3}+\sqrt{18})}\) \(-\cfrac{\sqrt{18}(3+\sqrt{12})}{(3-\sqrt{12})(3+\sqrt{12})}\)
\(=\cfrac{4\sqrt{3}(2+\sqrt{2})}{(2)^2-(\sqrt{2})^2}\) \(-\cfrac{30(4\sqrt{3}+\sqrt{18})}{(4\sqrt{3})^2-(\sqrt{18})^2}\) \(-\cfrac{\sqrt{18}(3+\sqrt{12})}{(3)^2-(\sqrt{12})^2}\)
\(=\cfrac{4\sqrt{3}(2+\sqrt{2})}{4-2}\) \(-\cfrac{30(4\sqrt{3}+\sqrt{18})}{48-18}\) \(-\cfrac{\sqrt{18}(3+\sqrt{12})}{9-12}\)
\(=\cfrac{4\sqrt{3}(2+\sqrt{2})}{2}\) \(-\cfrac{30(4\sqrt{3}+3\sqrt{2})}{30}\) \(-\cfrac{3\sqrt{2}(3+2\sqrt{3})}{-3}\)
\(=2\sqrt{3}(2+\sqrt{2})-(4\sqrt{3}+3\sqrt{2})\) \(+\sqrt{2}(3+2\sqrt{3})\)
\(=4\sqrt3+2\sqrt6-4\sqrt3-3\sqrt2+3\sqrt2+2\sqrt6\)
\(=4\sqrt6\)