simplfy
`((3+sqrt5)/(3-sqrt5))+((3-sqrt5)/(3+sqrt5))+((sqrt5-1)/(sqrt5+1))`

((4 +sqrt5)/(4-sqrt5)) +((4-sqrt5)/(4+sqrt5)) =?

Simplify each of the following : (i) 3/(5-sqrt(3))+2/(5+sqrt(3)) (ii) (4+sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (iii) (sqrt(5)-2)/(sqrt(5)+2)-(sqrt(5)+2)/(sqrt(5)-2)

Find sqrt(2+3sqrt(-5)) + sqrt(2-3sqrt(-5))

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

Simplify: (i) (7+3\ sqrt(5))/(3+\ sqrt(5))-(7-3\ sqrt(5))/(3-\ sqrt(5)) (ii) 1/(2+sqrt(3)\ )+2/(sqrt(5)-\ sqrt(3))+1/(2-\ sqrt(5))

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

((sqrt(5)-3))/((sqrt(5)-3))times((sqrt(5)-3))/((sqrt(5)+3))

Simplify: (i) (3sqrt(2)-2sqrt(2))/(3sqrt(2)+\ 2sqrt(3))+(sqrt(12))/(sqrt(3)-\ sqrt(2)) (ii) (sqrt(5)+\ sqrt(3))/(sqrt(5)-\ sqrt(3))+(sqrt(5)-\ sqrt(3))/(sqrt(5)+\ sqrt(3))

Simplify: (sqrt 3 - sqrt 5)(sqrt 5+ sqrt 3)

solve (3sqrt5 +sqrt3)/(sqrt5 -sqrt3)