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

Simplify (1)/(3 - sqrt(8)) - (1)/(sqrt(8) - sqrt(7)) + (1)/(sqrt(7) - sqrt(6)) - (1)/(sqrt(6) - sqrt(5)) + (1)/(sqrt(5) - 2)

Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+sqrt(3)) +(1)/(sqrt(3)+1)=1 (ii) (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+(1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7)) +(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8) + sqrt(9)) = 2

Simplify (1)/(7+4sqrt(3))+(1)/(2+sqrt(5))

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

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

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

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

The value of (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+1/(sqrt(3)+sqrt(4))+........+(1)/(sqrt(8) + sqrt(9)) is