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\(\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}\)

Note that

(  1)^3 - ( ∛3)^3  =   ( 1 - ∛3 ) ( 1 + ∛3 + (∛3)^2)  =     ( 1 - ∛3 )   ( 1 - ∛3 + ∛9)

So  this implies that if we multiply the numerator and  denominator by  ( 1 - ∛3)  we get

2∛9 ( 1 - ∛3)                         2 ∛9 - 2∛9 *∛3        2∛9 - 2∛27          2 [ ∛9 - 3 ]

__________________  = ______________  =  ___________  = ___________ =

( 1 - ∛3 + ∛9) ( 1 - ∛3)         (1)^3  - (∛3)^3            1  -  3                    -2

- [ ∛9 - 3 ]     =

3 - ∛9      [  =   3  - 3^(2/3) ]

See other solutions here, particularly answer # 11.

https://web2.0calc.com/questions/help-plzzzz_3