Answer: [tex]\frac{5\sqrt{3}-\sqrt{6}}{3}[/tex]
Step-by-step explanation:
1. You have the following expression given in the problem:
[tex]\frac{5-\sqrt{2}}{\sqrt{3}}[/tex]
2. To rationalize the denominator, you must multiply the numerator and the denominator by [tex]\sqrt{3}[/tex]:
[tex]=(\frac{5-\sqrt{2}}{\sqrt{3}})(\frac{\sqrt{3}}{\sqrt{3}})\\\\=\frac{5\sqrt{3}-\sqrt{(3)(2)}}{(\sqrt{3})^{2}}\\[/tex]
3. Then, you obtain the following result:
[tex]=\frac{5\sqrt{3}-\sqrt{6}}{3}[/tex]
