simplifying (8a) / (a^2 - b^2) + (2a) / (a^2 - ab)

   8a                2a
---------    +  --------
a^2 - b^2       a^2 + ab

You correctly factored the denominators, which is the first step in finding the common denominator:

      8a                 2a
-----------     +    -----------
(a + b)(a - b)       a(a + b)

Now...what is the common denominator for the two fractions?  It looks to me like the common denominator must contain these factors:  a (a + b)(a - b)

Your next step is to rewrite each fraction as an equivalent fraction with  a(a + b)(a - b) as its denominator.  To accomplish this, you'll need to multiply numerator and denominator of the first fraction by "a", and numerator and denominator of the second fraction by (a - b):


   8a(a)                 2a(a - b)
-----------     +   -----------------
(a+b)(a-b)a       (a+b)(a-b)a

NOW....the two fractions have the same denominator.  ADD the numerators, and put the result over the common denominator.