Verified answer

Given :

[tex] = \frac{1}{ \sqrt{3} - \sqrt{2} } \\ [/tex]

To do :

[tex]Rationalize[/tex]

Solution Explanation :

[tex] = \frac{1}{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ \\ = \frac{ \sqrt{3} + \sqrt{2} }{( \sqrt{3}) {}^{2} - ( \sqrt{2} ) {}^{2} } \\ \\ = \frac{ \sqrt{3} + \sqrt{2} }{3 - 2} \\ \\ = \frac{ \sqrt{3} + \sqrt{2} }{1} \\ \\ = \sqrt{3} + \sqrt{2} [/tex]

Answer:

[tex](1/\sqrt{3} ) - \sqrt{2} = \frac{-5\sqrt{3} }{3}[/tex]

Step-by-step explanation:

Given,

[tex]\frac{1}{\sqrt{3} } - \sqrt{2}[/tex]

Upon simplifying:

[tex]=\frac{1-6}{\sqrt{3} }[/tex]

[tex]=\frac{-5}{\sqrt{3} } \\=\frac{-5\sqrt{3} }{\sqrt{3}\sqrt{3} } \\\\=\frac{-5\sqrt{3} }{3}[/tex]