1. ## Rational exponents problem

I am supposed to factor
$\displaystyle 3(x-2)^{\frac{1}{2}}$ from $\displaystyle 12(x-2)^{\frac{3}{2}}-9(x-2)^{\frac{1}{2}}$

and my procedure was
$\displaystyle 12(x-2)^{\frac{3}{2}}-9(x-2)^{\frac{1}{2}}$

$\displaystyle 12(x-2)^{\frac{1}{2}+\frac{2}{2}}-9(x-2)^{\frac{1}{2}}$

$\displaystyle 3(x-2)^{\frac{1}{2}}[4(x-2)-3]$

I checked my result but the book I am working with says the answer should be $\displaystyle 3(x-2)^{\frac{1}{2}}(4x-11)$

Am I doing something wrong?? Please let me know.

2. Originally Posted by Alienis Back
I am supposed to factor
$\displaystyle 3(x-2)^{\frac{1}{2}}$ from $\displaystyle 12(x-2)^{\frac{3}{2}}-9(x-2)^{\frac{1}{2}}$

and my procedure was
$\displaystyle 12(x-2)^{\frac{3}{2}}-9(x-2)^{\frac{1}{2}}$

$\displaystyle 12(x-2)^{\frac{1}{2}+\frac{2}{2}}-9(x-2)^{\frac{1}{2}}$

$\displaystyle 3(x-2)^{\frac{1}{2}}[4(x-2)-3]$

I checked my result but the book I am working with says the answer should be $\displaystyle 3(x-2)^{\frac{1}{2}}(4x-11)$

Am I doing something wrong?? Please let me know.
your not doing anything wrong, $\displaystyle 4(x-2)-3=4x-11$