(sqrt(243))/(sqrt(3))=?

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)

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

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))

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))

(3sqrt(2))/(sqrt(3)+sqrt(6))-(4sqrt(3))/(sqrt(6)+sqrt(2))+(sqrt(6))/(sqrt(3)+sqrt(2))

(3sqrt(2))/(sqrt(6)-sqrt(3))+(2sqrt(3))/(sqrt(6)+2)-(4sqrt(3))/(sqrt(6)-sqrt(2))

Evaluate (sqrt46)/(sqrt(243)).

((2+sqrt(3))/(sqrt(2)+sqrt(2+sqrt(3)))+(2-sqrt(3))/(sqrt(2)+sqrt(2-sqrt(3))))^(2)=

([(sqrt(2)+i sqrt(3))+(sqrt(2)-i sqrt(3))])/([(sqrt(3)+1sqrt(2))+(sqrt(3)-1sqrt(2))])

If a=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)),b=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) then the value of a+b is