Question

Find a and b if both a and b are rational.`(sqrt(2) +sqrt(3))/(3sqrt(2) - 2sqrt(3))=a-bsqrt(6)`

Answer 1

`(sqrt2+sqrt3)/(3sqrt2-2sqrt3)`
`=(sqrt2+sqrt3)/((sqrt2sqrt3)(sqrt3+sqrt2))`
`=((sqrt2+sqrt3)sqrt6(sqrt3+sqrt2))/(sqrt6(sqrt3-sqrt2)sqrt6(sqrt3+sqrt2)`
`=((sqrt3+sqrt2)^2sqrt6)/(sqrt6((sqrt3)^2-(sqrt2)^2)`
`=(3+2+2sqrt6)/(6(3-2))`
`=(5/6+(2sqrt6)/6)sqrt6`
`=5/sqrt6+2`
`=5/sqrt6+sqrt6/sqrt6 +2`
`=5/6(sqrt6)+2`
`=2+5/6(sqrt6)`
`a=2`
`b=-5/6`