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

Here's how to simplify 4/(1 - 3^(1/3) + 9^(1/3)):

 

Recognize the Pattern: This expression involves the cube roots of 3 and 9. We know that 3^(1/3) = 3 and 9^(1/3) = 2.

 

Substitute the Values: Rewrite the expression with these values:

 

4 / (1 - 3 + 2)

 

Simplify the Denominator: Combine the terms in the denominator:

 

4 / (-1)

 

Division: Divide the numerator by the denominator:

 

4 / -1 = -4

 

Therefore, the simplified form of the expression is -4.