simplify the sum 7/(a + 8) + 7/(a^2 - 64)
To simplify the sum 7/(a + 8) + 7/(a^2 - 64), we need to find a common denominator.
The denominator of the first fraction is (a + 8) and the denominator of the second fraction is (a^2 - 64). Since (a^2 - 64) is a difference of squares, it can be factored as (a - 8)(a + 8).
The common denominator for the two fractions is (a + 8)(a - 8).
Now we rewrite the fractions with the common denominator:
7(a - 8)/((a + 8)(a - 8)) + 7/(a^2 - 64)
Now, we combine the numerators over the common denominator:
[7(a - 8) + 7]/((a + 8)(a - 8))
Simplify the numerator:
[7a - 56 + 7]/((a + 8)(a - 8))
(7a - 49)/((a + 8)(a - 8)).
Therefore, the simplified sum of 7/(a + 8) + 7/(a^2 - 64) is (7a - 49)/((a + 8)(a - 8)).