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Simplify \frac{4}{1 - \sqrt[3]{3}} + \sqrt[3]{9}.

 Dec 15, 2023
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\( \frac{4}{1 - \sqrt[3]{3}} + \sqrt[3]{9} \)

 

Note that    1 - 3    can be factored as a difference of  cubes  =   ( 1 - ∛3) ( 1 + ∛3 + ∛9)

 

Multiplting the denominator of the first fraction by  ( 1 + ∛3 + ∛9)  we have

 

[ 4  ( 1 + ∛3 + ∛9) ] /  [ 1 - 3 ]   +  ∛9   =

 

[ -2 (  ( 1 + ∛3 +∛9) ] + ∛9  =

 

-2 - 2 ∛3 - 3∛9

 

cool cool cool

 Dec 15, 2023

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