I need help with learning the steps to solving this problem.

http://i224.photobucket.com/albums/d...tt_Ford/2x.jpg

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- Nov 3rd 2007, 04:57 PMAshSimplifying a Complex Rational Expression
I need help with learning the steps to solving this problem.

http://i224.photobucket.com/albums/d...tt_Ford/2x.jpg - Nov 3rd 2007, 05:03 PMJhevon
- Nov 3rd 2007, 05:05 PMtopsquark
The first thing to do is to get rid of the fractions in the numerator. So what is the LCM of $\displaystyle a + b$ and $\displaystyle a - b$? $\displaystyle (a + b)(a - b)$, of course.

So we want to multiply the numerator of the complex fraction by $\displaystyle (a + b)(a - b)$, and thus we need to multiply the same thing in the denominator:

$\displaystyle \frac{ \frac{3}{a + b} - \frac{3}{a - b} }{2ab}$

$\displaystyle = \frac{ \frac{3}{a + b} - \frac{3}{a - b} }{2ab} \cdot \frac{(a + b)(a - b)}{(a + b)(a - b)}$

$\displaystyle = \frac{3(a - b) - 3(a + b) }{2ab(a + b)(a - b)}$

which you can simplify from here.

-Dan - Nov 3rd 2007, 05:29 PMAsh
So the answer would be -

__-6b___________

2ab(a+b) (a-b)

_ _______3__________

a( a + b) (a - b) - Nov 3rd 2007, 05:33 PMJhevon