Polynomial division

1. Sep 21, 2009

Hannisch

3rd roots in denominator

1. The problem statement, all variables and given/known data
$$\frac{ \sqrt[3]{25} + \sqrt[3]{5x} + \sqrt[3]{x^2} }{ \sqrt[3]{x} - \sqrt[3]{5} }$$

Rewrite the expression with no roots in the denominator and it being simplified as far as possible.

2. Relevant equations

3. The attempt at a solution
I'm.. stumped. Seriously. How on earth do I get rid of them? I can't do the conjugate, I can't take the denominator to the power of three, I can't take it times (x3 + 53) and I'm out of ideas.

Sorry about it being called Polynomial division, mishap on my behalf.

Last edited: Sep 21, 2009
2. Sep 21, 2009

ehild

Try to use the identity

y3-a3=(y-a)(y2+ay+a2)

ehild

3. Sep 22, 2009

Hannisch

Thank you! I'd never have figured that one out myself