hi, i am having trouble understanding some simplification my book is using. They take [3x/(3x-2)] and turn it into 1+[2/(3x-2)], can someone please explain how they did that?

thank you

Printable View

- Feb 25th 2008, 04:11 PMcowboys111help understanding simplification
hi, i am having trouble understanding some simplification my book is using. They take [3x/(3x-2)] and turn it into 1+[2/(3x-2)], can someone please explain how they did that?

thank you - Feb 25th 2008, 04:40 PMtopsquark
You can do a long division on it, or use a little trick:

$\displaystyle \frac{3x}{3x - 2} = \frac{3x - 2 + 2}{3x - 2} = \frac{3x - 2}{3x - 2} + \frac{2}{3x - 2}$

$\displaystyle = 1 + \frac{2}{3x - 2}$

Make sure you learn how to do the long division method as well.

-Dan - Feb 25th 2008, 04:47 PMcowboys111
awesome! thank you