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