Freeflows

Radical Expression Sum 2

If we write $ \sqrt{2}+\frac{1}{\sqrt{2}} + \sqrt{3} + \frac{1}{\sqrt{3}} $ in the form $ \dfrac{a\sqrt{2} + b\sqrt{3}}{c} $ such that $ a $, $ b $, and $ c $ are positive integers and $ c $ is as small as possible, then what is $ a+b+c $?

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+
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-
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9
$\frac{a}{b}$
.
0
=
%

$a^n$
$a^{\circ}$
$a_n$
$\sqrt{}$
$\sqrt[n]{}$
$\pi$
$\ln{}$
$\log$
$\theta$
$\sin{}$
$\cos{}$
$\tan{}$

$($
$)$
$[$
$]$
$\cap$
$\cup$
$,$
$\infty$

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