Final answer:
To add or subtract the given fractions, find the common denominator, which is (x+3)(x+3)(x-3). Expand and combine like terms, then simplify the equation to (7x+6)/((x+3)(x+3)(x-3)).
Step-by-step explanation:
To add or subtract the given fractions, we need to first find a common denominator. The denominators of the three fractions are (x+3), (x²+6x+9), and (x²-9).
To find the common denominator, we can factor each denominator and identify the common factors. The factors of (x+3) are (x+3) itself, the factors of (x²+6x+9) are (x+3)(x+3), and the factors of (x²-9) are (x+3)(x-3).
Therefore, the common denominator is (x+3)(x+3)(x-3). With the common denominator, we can now add/subtract the fractions.
Using the common denominator, the expression becomes (3(x-3)+(5(x+3))+(-x))/((x+3)(x+3)(x-3)).
Expanding and combining like terms, we get (3x-9+5x+15-x)/((x+3)(x+3)(x-3)).
Simplifying further, we have (7x+6)/((x+3)(x+3)(x-3)).