Simplify the complex fraction.

Question

n minus three over n squared plus six times n plus eight divided by n plus one over n plus two

(1 point)
Responses

n minus three over parenthesis n plus four parenthesis times parenthesis n plus one parenthesis
Image with alt text: n minus three over parenthesis n plus four parenthesis times parenthesis n plus one parenthesis

parenthesis n minus three parenthesis times parenthesis n plus two parenthesis over parenthesis n plus four parenthesis times parenthesis n plus one parenthesis
Image with alt text: parenthesis n minus three parenthesis times parenthesis n plus two parenthesis over parenthesis n plus four parenthesis times parenthesis n plus one parenthesis

n plus two over parenthesis n plus four parenthesis times parenthesis n plus one parenthesis
Image with alt text: n plus two over parenthesis n plus four parenthesis times parenthesis n plus one parenthesis

n minus four over parenthesis n plus four parenthesis times parenthesis n plus one parenthesis

Answer 1

To simplify the complex fraction, we multiply the numerator by the reciprocal of the denominator:

(n - 3)/(n + 4) * (n + 2)/(n + 1)

This simplifies to:

(n - 3)(n + 2) / (n + 4)(n + 1)

Which simplifies further to:

(n^2 - n - 6) / (n^2 + 5n + 4)