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Question
Simplify:
`sqrt2/[sqrt6 - sqrt2] - sqrt3/[sqrt6 + sqrt2]`
Solution
`sqrt2/[sqrt6 - sqrt2] - sqrt3/[sqrt6 + sqrt2]`
= `[ sqrt2]/[ sqrt6 - 2] - [ sqrt3 ]/[ sqrt6 + sqrt2 ] `
`= [ sqrt2( sqrt6 + sqrt2) - sqrt3( sqrt6 - sqrt2 )]/[ (sqrt6 - sqrt2)- (sqrt 6 + sqrt2)]`
= `[ sqrt12 + 2 - sqrt18 + sqrt6 ]/[ (sqrt6)^2 - (sqrt2)^2 ]`
= `[ 2sqrt3 + 2 - 3sqrt2 + sqrt6 ]/(6 - 2)`
= `[ 2sqrt3 + 2 - 3sqrt2 + sqrt6 ]/4`
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