Express each one of the following with rational denominator:
(i)`(sqrt(3)+ 1)/(2sqrt(2)- sqrt(3))` (ii) `(6-4sqrt(2))/(6+4sqrt(2))`

Explanation

`(i) (sqrt3+1)/((2sqrt2)-(sqrt3))`
`(sqrt3+1)/((2sqrt2)-(sqrt3))xx((2sqrt2)+(sqrt3))/((2sqrt2)+(sqrt3))`
`((sqrt3+1)(2sqrt2+sqrt3))/((2sqrt2)^2-(sqrt3)^2)`
`(sqrt3(2sqrt2)+(sqrt3)+1(2sqrt2)+(sqrt3))/(8-3)`
`(2sqrt6+sqrt3+2sqrt2+sqrt3)/5`
`(2sqrt3+2sqrt2+2sqrt6)/5`
`(ii) (6-4sqrt2)/(6+4sqrt2)`
`(6-4sqrt2)^2/((6)^2-(4sqrt2)^2)`
`(36+32-48sqrt2)/(36-32)`
`(68-48sqrt2)/4`
`(4xx(17-12sqrt2))/4`
`17-12sqrt2`