Bentuk sederhana dari \(\cfrac{2\sqrt{54}+4\sqrt{6}}{4\sqrt{8}-3\sqrt{2}}\) adalah....

\(\begin{aligned} \cfrac{2\sqrt{54}+4\sqrt{6}}{4\sqrt{8}-3\sqrt{2}} &= \cfrac{2\sqrt{9\times 6}+4\sqrt{6}}{4\sqrt{4\times 2}-3\sqrt{2}} \\ &= \cfrac{2\times 3\sqrt{6}+4\sqrt{6}}{4\times 2\sqrt{2}-3\sqrt{2}} \\ &= \cfrac{6\sqrt{6}+4\sqrt{6}}{8\sqrt{2}-3\sqrt{2}} \\ &= \cfrac{10\sqrt{6}}{5\sqrt{2}} \\ &= \cfrac{10\sqrt{3\times 2}}{5\sqrt{2}} \\ &= \cfrac{^2\cancel{10}\sqrt{3}\cancel{\sqrt{2}}}{\cancel{5}\cancel{\sqrt{2}}} \\ &= 2\sqrt{3} \end{aligned}\)