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[tex]\frac{1}{\sqrt{3}-1 } +\frac{1}{\sqrt{3}+1 }

Sagot :

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[ 1 / √3 - 1 ] + [ 1 / √3 + 1 ] =

[ ( √3 + 1 / √3 + 1 )( 1 / √3 - 1 ) ] +

[ ( √3 - 1 / √3 - 1 )( 1 / √3 + 1 ) ] =

[ √3 + 1 / ( √3 + 1 )( √3 - 1 ) ] +

[ √3 - 1 / ( √3 + 1 )( √3 - 1 ) ] =

√3 + 1 + √3 - 1 / ( √3 + 1 )( √3 - 1 ) =

2√3 / ( √3 )^2 - ( 1 )^2 =

2√3 / 3 - 1 =

2√3 / 2 =

2 × √3 / 2 × 1 =

√3

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