# Thread: How To Simplify...?

1. ## How To Simplify...?

Why does #1 become #2 and how?

#1

((3-x)^3)/(3x^(2/3)) - 3((3-x)^2)(x^(1/3))

#2

-(((x-3)^2)(10x-3))/(3x^(2/3))

I multiplied - 3((3-x)^2)(x^(1/3)) by the denominator ((3x^(2/3))), but still don't get why... or how.

2. Hello, AlphaRock!

Why does #1 become #2 and how?

#1: .$\displaystyle \frac{(3-x)^3}{3x^{\frac{2}{3}}} - 3(3-x)^2x^{\frac{1}{3}}$

#2: .$\displaystyle -\,\frac{(x-3)^2(10x-3)}{3x^{\frac{2}{3}}}$
We have: .$\displaystyle \frac{(3-x)^2}{3x^{\frac{2}{3}}} - 3(3-x)^2x^{\frac{1}{3}}$

Get a common denominator: .$\displaystyle \frac{(3-x)^3}{3x^{\frac{1}{3}}} \;- \;\frac{3(3-x)^2x^{\frac{1}{3}}}{1}\cdot{\color{blue}\frac{3x^ {\frac{2}{3}}}{3x^{\frac{2}{3}}}}$

. . . . . $\displaystyle = \;\;\frac{(3-x)^3}{3x^{\frac{2}{3}}} - \frac{9x(3-x)^2}{3x^{\frac{2}{3}}} \;\;=\;\;\frac{(3-x)^3 - 9x(3-x)^2}{3x^{\frac{2}{3}}}$

Factor: .$\displaystyle \frac{(3-x)^2\bigg[(3-x) - 9x\bigg]}{3x^{\frac{2}{3}}} \;\;=\;\;\frac{(3-x)^2\bigg[-10x + 3\bigg]}{3x^{\frac{2}{3}}}$

Factor out -1: .$\displaystyle -\,\frac{(x-3)^2(10x-3)}{3x^{\frac{2}{3}}}$