Simplify and rationalize the denominator: 1/(1 + 1/(sqrt(3) + 2)).
1 / ( 1 + 1/sqrt (3) + 2) =
1/ ( 3 + 1/sqrt (3) ) =
sqrt (3) / ( 3sqrt (3) + 1 ) multiply numerator /denominator by 3sqrt (3) - 1
sqrt (3) ( 3sqrt (3) - 1)
__________________ =
9*3 - 1
9 - sqrt (3)
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