simplify
`(sqrt3 +1)/(sqrt3 -1) + (sqrt3 -1)/(sqrt3 +1)`

Simplify: (3+sqrt 3)(3-sqrt3)

Rationalize the denominator: (2 + sqrt 3)/(2 - sqrt 3) + (2 - sqrt 3)/(2 + sqrt 3) + (sqrt 3 - 1)/(sqrt 3 + 1)

Simplify: 1/(sqrt5 + sqrt4) + 1/(sqrt4 + sqrt3) + 1/(sqrt3 + sqrt2) + 1/(sqrt2 + sqrt1)

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

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

If sqrt(3) = 1.73 find the value of : (2+sqrt(3))/(2-sqrt(3))+(2-sqrt(3))/(2+sqrt(3))+(sqrt(3)-1)/(sqrt(3)+1)-(sqrt(3)+1)/(sqrt(3)-1) .

Simplify : (22)/(2sqrt(3)+1)+(17)/(2sqrt(3)-1)

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

Simplify: (sqrt3/2)^2 -(sqrt3)^2+(sqrt 2)^2 +1/2

The area of the triangle formed by three point sqrt3 +i, -1+sqrt3i and (sqrt3-1) +(sqrt3+1)i is ________