[tex]x= \sqrt{3} \\\\
y= \frac{1}{ \sqrt{3} } \\\\
\frac{x}{y} + \frac{y}{x} = \frac{10}{3} \\\\
\frac{ \frac{1}{ \sqrt{3} } }{ \sqrt{3} } + \frac{ \frac{1}{ \sqrt{3} } }{ \sqrt{3} } = \frac{ \sqrt{3} }{1} * \frac{ \sqrt{3} }{1} + \frac{1}{ \sqrt{3} } * \frac{1}{ \sqrt{3} } \\\\
= \frac{ \sqrt{9} }{1} + \frac{1}{ \sqrt{9} } = \frac{3}{1} + \frac{1}{3} = \frac{3*3}{1*3} + \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3}
[/tex]
