How to Rationalize the Denominator of a Radical Expression?

[The legend]

Homework Statement

Rationalize the denominator..
$$\frac{1}{\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}}$$

Homework Equations

Algebraic equations.

The Attempt at a Solution

So using the form
a³ + b³ + c³ - 3abc= (a + b + c)(a² + b² + c² - ab - bc - ca)

So it becomes


$$\frac{\sqrt[3]{a^2}+\sqrt[3]{b^2}+\sqrt[3]{c^2} -\sqrt[3]{ab}-\sqrt[3]{bc}-\sqrt[3]{ca} }{a + b + c - 3 \sqrt[3]{abc}}$$


Actually I don't know what to do next
If i try (a+b)(a-b) then it doesn't work out ...

 

[ehild]

Use

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

ehild

 

[Mark44]

Use

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

ehild

I don't see how this applies to the OP's problem.

 

[Mentallic]

Use

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

ehild

I don't see how this applies to the OP's problem.

$$x-y=\frac{x^3-y^3}{x^2+xy+y^2}$$

 

[Mark44]

Good thing you put in the wink emoticon.

 

[Mentallic]

Of course! An emoticon is worth a thousands words.

If there were a more suitable emoticon for "I'm sure you get it now" I would use that one instead.

<< (don't kill me for this )

 

[The legend]

Yup got it!
Thanks!

(Checked it out with my teacher ... its right!)