Polynomial Division: Simplifying 3rd Roots in Denominator

[Hannisch]

3rd roots in denominator

Homework Statement

$$\frac{ \sqrt[3]{25} + \sqrt[3]{5x} + \sqrt[3]{x^2} }{ \sqrt[3]{x} - \sqrt[3]{5} }$$

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

Homework Equations

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.

 

[ehild]

Try to use the identity

y³-a³=(y-a)(y²+ay+a²)

ehild

 

[Hannisch]

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