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Add or subtract as indicated. If possible, simplify your answer. (3)/(x+3)+(5)/(x²+6x+9)-(x)/(x²-9)

User Jlstr
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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)).

User Zhang Chao
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