Simplify the expression.

Question

7/n-3 + n/n+3=?

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

Answer 1

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) = n² - 9
Both fractions must have n²-9 in the denominator and then you can add the numerators
7/(n-3)  times (n+3)/(n+3) = 7 (n+3)/(n²-9)
n/(n+3) times (n-3)/(n-3)  = n (n-3)/(n²-9)
Result is [7(n+3) + n(n-3)]/(n²-9)
The numerator is 7n + 21 + n² - 3n = n² + 4n + 21, denominator is n²-9 = (n+3)(n-3) in factored form

Final answer:  (n² + 4n + 21)/(n+3)(n-3)