`frac{sqrt5+1}{sqrt5-1}+frac{sqrt5-1}{sqrt5+1}`=?

frac{1}{sqrt7-4} frac{1}{sqrt11-7}

2sqrt5 - sqrt5 = sqrt5

solve the equations: frac{2}{sqrt x} + frac{3}{sqrt y} =2 and frac{4}{sqrt x} - frac{9}{sqrt y} =-1

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

a=9-4sqrt(5) , sqrt(a)-1/sqrt(a)=?

sqrt(5){(sqrt(5)+1)^(50)-(sqrt(5)-1)^(50)}

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

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))

(iii) (sqrt 5+ sqrt 3)/(sqrt5-sqrt3)+(sqrt5-sqrt3)/(sqrt5+sqrt3) =?

Simplify (sqrt5-sqrt2)(sqrt5+sqrt2)