Simplify `((4)/(sqrt(5)+1))^(2)+((1)/(sqrt5-1))^(2)+2(4)/(sqrt5+1)times(1)/(sqrt5-1)`

(sqrt(5)-1)/(sqrt(5)+1)+(sqrt(5)+1)/(sqrt(5)-1)

{(sqrt(2) +1)^(5) + (sqrt(2) -1)^(5)}=

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

(1)/(2+sqrt(3))+(2)/(sqrt(5)-sqrt(3))+(1)/(2-sqrt(5))=0

Simplify (1)/(sqrt(6)-sqrt(5))+sqrt(6)-sqrt(5)

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

Prove:- ((sqrt5-1)/4)^2 ((sqrt5+1)/4)^2 =(1/16)

Simplify (i) (4+ sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (ii) (1)/(sqrt(3) + sqrt(2)) - (2)/(sqrt(5)-sqrt(3)) -(2)/(sqrt(2) - sqrt(5)) (iii) (2+sqrt(3))/(2-sqrt(3)) + (2-sqrt(3))/(2+sqrt(3)) + (sqrt(3)-1)/(sqrt(3)+1) (iv) (2+sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3)) -(8sqrt(3))/(sqrt(6)+sqrt(2))

(iii) simplify (2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))