a) [tex]\frac{3}{2}\sqrt{6}+2\sqrt{\frac{2}{3}}-4\sqrt{\frac{3}{2}}=\frac{3}{2}\sqrt{6}+2\frac{\sqrt{6}}{3}-4\frac{\sqrt{6}}{2}=\sqrt{6}(\frac{3}{2}+\frac{2}{3}-2)=\frac{\sqrt{6}}{6}[/tex]
b) [tex](x\sqrt{\frac{6}{x}}+\sqrt{\frac{2x}{3}}+\sqrt{6x}):\sqrt{6x}=\sqrt{x}(\sqrt{6}+\sqrt{\frac{2}{3}}+\sqrt{6}).\frac{1}{\sqrt{6x}}=\frac{2\sqrt{6}+\sqrt{\frac{2}{3}}}{\sqrt{6}}=\frac{\sqrt{6}(2+\frac{1}{3})}{\sqrt{6}}=\frac{7}{3}=2\tfrac{1}{3}[/tex]