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

(sqrt(5)-2)(sqrt(3)-sqrt(5))

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

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

Find ( sqrt(5) + 1 )/( sqrt(5 ) - 1) = ( A ) ( 3 + sqrt(5) )/2 ( A ) ( 3 - sqrt(5) )/2 ( A ) ( 3 + sqrt(5) )/4 ( A ) ( 3 - sqrt(5) )/4

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

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

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

The domain of f(x)=sin^(-1)[2x^(2)-3], where [.] denotes the greatest integer function,is (-sqrt((3)/(2)),sqrt((3)/(2)))uu(-sqrt((5)/(2)),sqrt((5)/(2)))(-sqrt((3)/(2)),-1)uu(-sqrt((5)/(2)),-1)uu(1,sqrt((5)/(2)))(-sqrt((5)/(2)),sqrt((5)/(2)))(-sqrt((5)/(2)),-1)uu(1,sqrt((5)/(2)))

Simplify each of the following by rationalising the denominator,(1)/(5+sqrt(2)) (ii) (5+sqrt(6))/(5-sqrt(6)) (iii) (7+3sqrt(5))/(7-3sqrt(5)) (iv) (2sqrt(3)-sqrt(5))/(2sqrt(2)+3sqrt(3))