+367 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, c and d are positive integers and c is as small as possible, then what is \(a+b+c\)?
+37146 (1) sqrt2 + 1/2 sqrt2 + (1) sqrt3 + 1/3 sqrt3 =
3/2 * sqrt2 + 4/3 * sqrt 3 =
9 sqrt2 + 8 sqrt 3
6
