# Thread: Simplifying a Complex Rational Expression

1. ## Simplifying a Complex Rational Expression

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

2. Originally Posted by Ash
I need help with learning the steps to solving this problem.
multiply the numerator and denominator of the whole fraction through by the product of the denominators of the fractions in the numerator. that is, multiply the top and bottom by (a + b)(a - b). can you take it from there?

3. Originally Posted by Ash
I need help with learning the steps to solving this problem.
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

4. So the answer would be -

-6b_________
2ab(a+b) (a-b)

_ _____3________
a( a + b) (a - b)

5. Originally Posted by Ash
So the answer would be -

-6b_________
2ab(a+b) (a-b)

_ _____3________
a( a + b) (a - b)
yes