# Math Help - Express as a sum of terms of the form ax^r, where r is a rational number

1. ## Express as a sum of terms of the form ax^r, where r is a rational number

The book lacks any explanation of how to do this or what it means.

"Express as a sum of terms of the form ax^r, where r is a rational number"

1. (4x^2 - x + 5) / x^(2/3)

2. (x^2 + 2)^2 / x^5

1. 4x^(4/3) - x^(1/3) + 5x^-(2/3)

2. x^-1 + 4x^-3 + 4x^-5

I haven't the faintest idea of how to begin this or how the answers were derived. Help would be appreciated.

Thanks

2. Originally Posted by sstecken
The book lacks any explanation of how to do this or what it means.

"Express as a sum of terms of the form ax^r, where r is a rational number"

1. (4x^2 - x + 5) / x^(2/3)

2. (x^2 + 2)^2 / x^5

1. 4x^(4/3) - x^(1/3) + 5x^-(2/3)

2. x^-1 + 4x^-3 + 4x^-5

I haven't the faintest idea of how to begin this or how the answers were derived. Help would be appreciated.

Thanks
1. $\frac{4x^2-x+5}{x^{\tfrac{2}{3}}}$

All you need to do is rewrite this so each term has the form $ax^r$

So...

$\frac{4x^2-x+5}{x^{\tfrac{2}{3}}}=4\frac{x^2}{x^{\tfrac{2}{3} }}-\frac{x}{x^{\tfrac{2}{3}}}+5\frac{1}{x^{\tfrac{2}{ 3}}}=\color{red}\boxed{4x^{\tfrac{4}{3}}-x^{\tfrac{1}{3}}+5x^{-\tfrac{2}{3}}}$

Does this make sense?

Try the second one, and post what you did. Note that you will have to foil out the numerator first, and then split up the fraction.

I hope this makes more sense to you now!

--Chris

3. Awesome, makes perfect sense now. Thanks!