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

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

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

Simplify: (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(5))

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

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

Rationalise the denominator of each of the following. (i) (1)/(sqrt(7)) (ii) (sqrt(5))/(2sqrt(3)) (iii) (1)/(2+ sqrt(3)) (1)/(sqrt(3)) (v) (1)/((5+3sqrt(2)) (vi) (1)/(sqrt(7) - sqrt(6)) (vi) (1)/(sqrt(7) - sqrt(6)) (viii) (1+ sqrt(2))/(2-sqrt(2)) (ix) (3-2sqrt(2))/(3+2sqrt(2))

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

5.Simplify: (1/sqrt 2)/((2/sqrt3)+2)

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

(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))