`\qquad (2+sqrt{3})/(sqrt{2}+sqrt{2+sqrt{3}})+(2-sqrt{3})/(sqrt{2}-sqrt{2-sqrt{3}})`
`=(2sqrt{2}+sqrt{6})/(2+sqrt{4+2sqrt{3}})+(2sqrt{2}-sqrt{6})/(2-sqrt{4-2sqrt{3}})`
`=(2sqrt{2}+sqrt{6})/(2+sqrt{(sqrt{3}+1)^2})+(2sqrt{2}-sqrt{6})/(2-sqrt{(sqrt{3}-1)^2})`
`=(2sqrt{2}+sqrt{6})/(3+sqrt{3})+(2sqrt{2}-sqrt{6})/(3-sqrt{3})`
`=((2sqrt{2}+sqrt{6})(3-sqrt{3})+(2sqrt{2}-sqrt{6})(3+sqrt{3}))/(9-3)`
`=(6sqrt{2}-2sqrt{6}+3sqrt{6}-3sqrt{2}+6sqrt{2}+2sqrt{6}-3sqrt{6}-3sqrt{2})/6`
`=(6sqrt{2})/6`
`=sqrt{2}`