7. [tex](\sqrt[4]{27} + \sqrt[4]{3})*\sqrt[4]{3} - \sqrt{3} = \sqrt[4]{81}+\sqrt[4]{9} - \sqrt{3} = \sqrt[4]{3^4} + \sqrt[4]{3^2} - \sqrt{3} = 3 + \sqrt{3} - \sqrt{3} = 3[/tex]

8. [tex]\frac{2}{2+\sqrt{2}} = \frac{2(2-\sqrt{2})}{(2+\sqrt{2})(2-\sqrt{2})} = \frac{4-2\sqrt{2}}{4-2} = \frac{4-2\sqrt{2}}{2}[/tex]

9.

[tex]y = \sqrt[6]{\frac{x-2}{x}}\\\\\left \{ {{x!=0} \atop {\frac{x-2}{x} > =0}} \right. < = > \left \{ {{x!=0} \atop {x > =2}} \atop {x < 0} \right. \\\\[/tex]

Ответ: (-∞;0)∪[2;∞)