`x=(sqrt3-2)/(sqrt3+2)`
`=((sqrt3-2)(sqrt3+2))/(3-4)`
`=(sqrt3-2)^2/(-1)`
`=-(sqrt3-2)^2`
`=>x+2/x`
`=-(sqrt3-2)^2+2/x`
`=-(sqrt3-2)^2+(2(sqrt3+2)^2)/(-1)`
`=-(sqrt3-2)^2-2(sqrt3+2)^2`
`=-7+4sqrt3-14-8sqrt3`
`=-21-4sqrt3`
\(x\) = \(\dfrac{\sqrt{3}-2}{2+\sqrt{3}}\)
\(x\) = \(\dfrac{\sqrt{3}-2}{\sqrt{3}+2}\)
\(x\) = \(\dfrac{\left(\sqrt{3}-2\right)^2}{3-4}\)
\(x\) = \(4\sqrt{3}-7\)
\(x+\dfrac{2}{x}=4\sqrt{3}-7+\dfrac{2}{4\sqrt{3}-7}\)
\(=\dfrac{\left(4\sqrt{3}-7\right)^2+2}{4\sqrt{3}-7}\)
\(=\dfrac{99-56\sqrt{3}}{4\sqrt{3}-7}\)
\(=-21-4\sqrt{3}\)
