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(4sqrt(3)+5sqrt(2))/(sqrt(48)+sqrt(18))...

`(4sqrt(3)+5sqrt(2))/(sqrt(48)+sqrt(18))`

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`(4sqrt3+5sqrt2)/(sqrt48+sqrt18`
`(4sqrt3+5sqrt2)/(4sqrt3+3sqrt2)*(4sqrt3-3sqrt2)/(4sqrt3-3sqrt2)`
`(48+20sqrt6-12sqrt6-30)/(48-18)`
`(18+8sqrt6)/30`
`(9+4sqrt6)/15`.
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