7/n-3 + n/n+3=?

(Simplify your answer. Type your answer in factored form.)

7/n-3 + n/n+3=?

(Simplify your answer. Type your answer in factored form.)

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This problem should be written as 7/(n-3) + n/(n+3) = ?

The common denominator of (n-3) and (n+3) is their product: (n-3)(n+3) = n^{2} - 9

Both fractions must have n^{2}-9 in the denominator and then you can add the numerators

7/(n-3) times (n+3)/(n+3) = 7 (n+3)/(n^{2}-9)

n/(n+3) times (n-3)/(n-3) = n (n-3)/(n^{2}-9)

Result is [7(n+3) + n(n-3)]/(n^{2}-9)

The numerator is 7n + 21 + n^{2} - 3n = n^{2} + 4n + 21, denominator is n^{2}-9 = (n+3)(n-3) in factored form

Final answer: (n^{2} + 4n + 21)/(n+3)(n-3)

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