Simplify the complex fraction.
n minus three over n squared plus six times n plus eight divided by n plus one over n plus two
To simplify the complex fraction, first multiply the numerator and the denominator by the reciprocal of the denominator in the complex fraction:
= [ (n-3) / (n^2 + 6) ] * [ (n+2) / (n+1) ]
Now multiply the numerators and denominators:
= (n-3)(n+2) / (n^2 + 6)(n+1)
= (n^2 - n + 2n - 6) / (n^3 + n^2 + 6n + 6)
= (n^2 + n - 6) / (n^3 + n^2 + 6n + 6)
Therefore, the simplified complex fraction is (n^2 + n - 6) / (n^3 + n^2 + 6n + 6)
Are you sure?
I apologize for the mistake in my previous response. Let's reevaluate the simplification of the complex fraction:
The given complex fraction is:
(n - 3) / (n^2 + 6) * (n + 8) / (n + 1) / (n + 2) / (n + 1)
To simplify this complex fraction, we can combine the numerators and denominators of the fractions, and then multiply the fractions:
= (n - 3)(n + 8) / (n^2 + 6)(n + 1) * (n + 1) / (n + 2)
= (n^2 + 8n - 3n - 24) / ((n^2 + 6)(n+1)(n + 2))
= (n^2 + 5n - 24) / (n^3 + 2n^2 + 6n^2 + 12n + 6n + 12)
= (n^2 + 5n - 24) / (n^3 + 8n^2 + 18n + 12)
So, the simplified complex fraction is (n^2 + 5n - 24) / (n^3 + 8n^2 + 18n + 12).