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(1/2+1/7-2/sqrt3)/(2/sqrt3+1/2+1)...

`(1/2+1/7-2/sqrt3)/(2/sqrt3+1/2+1)`

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Simplify (1/2+1/sqrt2-sqrt3)/(sqrt3-1/sqrt2-1/sqrt3)

(sqrt3 + 1/sqrt3)^2

1/(1-sqrt2-sqrt3)=

((2+sqrt(3))/2)/(1+(sqrt(3)+1)/2) + ((2-sqrt(3))/2)/(1-((sqrt(3)-1)/2))

(-sqrt(3)/2 + sqrt(3))/(1/sqrt(2)-1)=

(sqrt3 + 1)/(2sqrt2) + (sqrt3 - 1)/(2sqrt2)

The value of (2 + sqrt(3))/(2- sqrt(3)) + (2- sqrt(3))/(2 + sqrt(3)) + ( sqrt(3) + 1)/(sqrt(3) -1) is

1/(1+ sqrt2 + sqrt3)