[tex]\dfrac{4\sqrt{18}-6\sqrt{6}}{3\sqrt{2}+2\sqrt{6}}=\bf14\sqrt{3}\ -\ 24[/tex]
Pembahasan
[tex]\begin{aligned}&\frac{4\sqrt{18}-6\sqrt{6}}{3\sqrt{2}+2\sqrt{6}}\\&{=\ }\frac{2\sqrt{2}\cdot\sqrt{2}\sqrt{18}-2\sqrt{2}\cdot3\sqrt{3}}{3\sqrt{2}+2\sqrt{3}\sqrt{2}}\\&{=\ }\frac{2\cancel{\sqrt{2}}\left(\sqrt{2}\sqrt{18}-3\sqrt{3}\right)}{\cancel{\sqrt{2}}\left(3+2\sqrt{3}\right)}\\&{=\ }\frac{2\left(\sqrt{2}\sqrt{3}\sqrt{6}-3\sqrt{3}\right)}{\sqrt{3}\sqrt{3}+2\sqrt{3}}\\&{=\ }\frac{2\cancel{\sqrt{3}}\left(\sqrt{2}\sqrt{6}-3\right)}{\cancel{\sqrt{3}}\left(\sqrt{3}+2\right)}\end{aligned}[/tex]
[tex]\begin{aligned}&{=\ }\frac{2\left(\sqrt{2}\sqrt{6}-3\right)}{\sqrt{3}+2}\\&{=\ }\frac{2\left(\sqrt{2}\sqrt{2}\sqrt{3}-\sqrt{3}\sqrt{3}\right)}{\sqrt{3}+2}\\&{=\ }\frac{2\sqrt{3}\left(2-\sqrt{3}\right)}{\sqrt{3}+2}\times\frac{\sqrt{3}-2}{\sqrt{3}-2}\\&{=\ }\frac{2\sqrt{3}\left(2-\sqrt{3}\right)\left(\sqrt{3}-2\right)}{\left(\sqrt{3}\right)^2-2^2}\\&{=\ }\frac{2\sqrt{3}\left(2\sqrt{3}-3-4+2\sqrt{3}\right)}{3-4}\\&{=\ }\frac{2\sqrt{3}\left(4\sqrt{3}-7\right)}{-1}\end{aligned}[/tex]
[tex]\begin{aligned}&{=\ }{-}\left(2\sqrt{3}\cdot4\sqrt{3}-2\sqrt{3}\cdot7\right)\\&{=\ }{-}\left(8\cdot3-14\sqrt{3}\right)\\&{=\ }{-}\left(24-14\sqrt{3}\right)\\&{=\ }\boxed{\ \bf14\sqrt{3}\ -\ 24\ }\end{aligned}[/tex]
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