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Simplify and rationalize the denominator: 1/(1 + 1/(sqrt(3) + 2)).

 Jul 28, 2022
 #1
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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)

________

      26

 

 

 

cool cool cool

 Jul 28, 2022

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