Rationaize the denominator 1/(2-4^1/3)

in other words it is one divided by 2 minus the cubed root of 4
plz help me with this it would be great if you can show the steps
thank you in advance :)

Rationalize 1/(2-4^(1/3)).

Use the difference of two cubes formula to rationalize.

x^3-y^3 = (x-y)(x^2+xy+y^2)

Let x=2 and y=4^(1/3). Multiply the numerator & denominator by (x^2+xy+y^2).

1/(2-4^(1/3)) * (4+2*4^(1/3)+4^(2/3))/(4+2*4^(1/3)+4^(2/…

(4+2*4^(1/3)+4^(2/3)/(8+4*4^(1/3)+2*4^…

Cancel out terms in the denominator to get:

(4+2*4^(1/3)+4^(2/3))/8-4

(4+2*4^(1/3)+4^(2/3))/4

1+(1/2)*4^(1/3)+(1/4)*4^(2/3)

rationalize(1/(2 - 4^(1/3))) = 1 + (1/2)*4^(1/3) + (1/4)*4^(2/3)