Solve
`(1) (sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))=a+bsqrt15`
`(2) (sqrt3-sqrt2)/(sqrt3+sqrt2)=a-bsqrt6`
`(3) (4+2sqrt5)/(4-3sqrt5)=a+bsqrt5`

3/(sqrt3-sqrt2)=asqrt3-bsqrt2

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

(2+sqrt(3))/(2-sqrt(3))=a+bsqrt(3)

(sqrt2+sqrt7)/(sqrt2-sqrt7)=a+bsqrt(14)

(2sqrt3 + sqrt5)(2sqrt3 - sqrt5)

If (4+2sqrt5)/(4-3sqrt5) = a+bsqrt5 ,then

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

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

(2)/(sqrt(3)+sqrt(5))+(5)/(sqrt(3)-sqrt(5))=x sqrt(3)+y sqrt(5)

Find rational numbers a and b such that (i) (sqrt2-1)/(sqrt2+1)=a+bsqrt2 (ii) (2-sqrt5)/(2+sqrt5)=asqrt5+b (iii) (sqrt3+sqrt2)/(sqrt3-sqrt2)=a+bsqrt6 (iv) (5+2sqrt3)/(7+4sqrt3)=a+bsqrt3