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Simplify the expression.

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1 Answer

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)