# Homework Help: Rationalize the denominator

1. Jul 21, 2010

### The legend

1. The problem statement, all variables and given/known data
Rationalize the denominator..
$$\frac{1}{\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}}$$

2. Relevant equations

Algebraic equations.

3. 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 dunno what to do next
If i try (a+b)(a-b) then it doesnt work out ...

2. Jul 21, 2010

### ehild

Re: Rationalize!!

Use

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

ehild

3. Jul 21, 2010

### Staff: Mentor

Re: Rationalize!!

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

4. Jul 21, 2010

### Mentallic

Re: Rationalize!!

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

5. Jul 21, 2010

### Staff: Mentor

Re: Rationalize!!

Good thing you put in the wink emoticon.

6. Jul 21, 2010

### Mentallic

Re: Rationalize!!

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 :tongue:)

7. Jul 25, 2010

### The legend

Re: Rationalize!!

Yup got it!
Thanks!

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