`x=2/(2+\sqrt{3})`
`⇔x=2(2-\sqrt{3})`
`⇔x=4-2\sqrt{3}`
`⇒\sqrt{x}=\sqrt{3-2\sqrt{3}+1}`
`⇔\sqrt{x}=\sqrt{(\sqrt{3}-1)^2}`
`⇔\sqrt{x}=\sqrt{3}-1`
`⇒(2\sqrt{x})/(x+1)`
`⇔(2(\sqrt{3}-1))/(4-2\sqrt{3}+1)`
`⇔(2\sqrt{3}-2)/(5-2\sqrt{3})`
`⇔[(2\sqrt{3}-2)(5+2\sqrt{3})]/(25-12)`
`⇔(10\sqrt{3}-10+12-4\sqrt{3})/13`
`⇔(6\sqrt{3}+2)/13`