Algebra

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

We can write  (1 - 3)  as  ( 1 - 3^(1/3))  ( 1 + 3^(1/3) + 3^(2/3) )

Mulitiplying the numerator and  denominator of the first fraction by the last factor in red we get

4 [ 1 + 3^(1/3) + 3^(2/3) ]          -2 [ 1 + 3^(1/3) + 3^(2/3) ]

____________________  =  

               1 - 3

And  9^(1/3)  = ( 3^2)^(1/3)  =  3^(2/3)

So we have

 -2 [ 1 + 3^(1/3) + 3^(2/3) ] + 3^(2/3)   =

-2  - 2*3^(1/3) - 3^(2/3)