`(2sqrt(7))/(sqrt(5)-sqrt(3))`

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))

If both a and b are rational numbers,find the values of a and b in each of the following equalities :(sqrt(3)-1)/(sqrt(3)+1)=a+b sqrt(3)( ii) (3+sqrt(7))/(3-sqrt(7))=a+b sqrt(7)(5+2sqrt(3))/(7+4sqrt(3))=a+b sqrt(3)( iv) (5+sqrt(3))/(7-sqrt(3))=47a+sqrt(3)b(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))=a+b sqrt(15) (iv) (sqrt(2)+sqrt(3))/(3sqrt(2)-2sqrt(3))=1-b sqrt(3)

If x=(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3)) and y=(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(2)), then x+y+xy=9(b)5(c)17(d)7, then

Simplify: (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))

7/(sqrt5-sqrt3) =

(sqrt(5)+sqrt(3))(sqrt(7)-sqrt(3))

The value of (2sqrt(10))/(sqrt(5)+sqrt(2)-sqrt(7))-sqrt((sqrt(5)-2)/(sqrt(5)+2))-3/(sqrt(7)-2) is

Rationales the denominator and simplify: (sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) (ii) (5+2sqrt(3))/(7+4sqrt(3)) (iii) (1+sqrt(2))/(3-2sqrt(2)) (2sqrt(6)-sqrt(5))/(3sqrt(5)-2sqrt(6)) (v) (4sqrt(3)+5sqrt(2))/(sqrt(48)+sqrt(18)) (vi) (2sqrt(3)-sqrt(5))/(2sqrt(3)+3sqrt(3))

Simplify: (7sqrt(3))/(sqrt(10)+sqrt(3))-(2sqrt(5))/(sqrt(6)+sqrt(5))-(3sqrt(2))/(sqrt(15)+3sqrt(2))