Simplify the following complex fraction::?
Simplify the following complex fraction:
[ \frac{n - 6}{n^2 + 11n + 24} \div \frac{n + 1}{n + 3} ]
1 Answers
Jan 25, 2025
[(n – 6) / (n^2 + 11n + 24)] / [(n + 1) / (n + 3)]
Factor “n^2 + 11n + 24” to get (n + 3)(n + 8). Now we have:
[(n – 6) / ((n + 3)(n + 8))] / [(n + 1) / (n + 3)]
Multiply by the reciprocal of the denominator.
[(n – 6) / ((n + 3)(n + 8))] * [(n + 3) / (n + 1)]
The (n + 3) terms cancel, so you are left with:
[(n – 6) / (n + 8)] * [1 / (n + 1)] = (n – 6) / [(n + 8)(n + 1)]
Solution: (n – 6) / [(n + 8)(n + 1)]
or
n – 6
——————-
(n + 8)(n + 1)
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