Answer:
The correct option is A) [tex]2\sqrt[3]{3}-{\sqrt[3]{18}[/tex]
Step-by-step explanation:
Consider the provided expression.
[tex]\frac{\left(6-3\left(\sqrt[3]{6}\right)\right)}{\sqrt[3]{9}}[/tex]
Rationalize by multiplying conjugate [tex]\frac{9^{\frac{2}{3}}}{9^{\frac{2}{3}}}[/tex]
[tex]\frac{\left(6-3\sqrt[3]{6}\right)\cdot \:9^{\frac{2}{3}}}{\sqrt[3]{9}\cdot \:9^{\frac{2}{3}}}[/tex]
[tex]\frac{9^{\frac{2}{3}}\cdot \:3\left(2-\sqrt[3]{6}\right)}{9}[/tex]
[tex]\frac{9^{\frac{2}{3}}\left(2-\sqrt[3]{6}\right)}{3}[/tex]
[tex]\frac{3^{\frac{4}{3}}\left(2-\sqrt[3]{6}\right)}{3}[/tex]
[tex]3^{\frac{1}{3}}\left(2-\sqrt[3]{6}\right)[/tex]
[tex]2\sqrt[3]{3}-3^{\frac{2}{3}}\sqrt[3]{2}[/tex]
[tex]2\sqrt[3]{3}-{\sqrt[3]{18}[/tex]
Hence, the correct option is A) [tex]2\sqrt[3]{3}-{\sqrt[3]{18}[/tex]
