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\frac{\left(n-3\right)\left(n+2\right)}{\left(n^{2}+6n+8\right)\left(n+1\right)}
Divide \frac{n-3}{n^{2}+6n+8} by \frac{n+1}{n+2} by multiplying \frac{n-3}{n^{2}+6n+8} by the reciprocal of \frac{n+1}{n+2}.
\frac{\left(n-3\right)\left(n+2\right)}{\left(n+1\right)\left(n+2\right)\left(n+4\right)}
Factor the expressions that are not already factored.
\frac{n-3}{\left(n+1\right)\left(n+4\right)}
Cancel out n+2 in both numerator and denominator.
\frac{n-3}{n^{2}+5n+4}
Expand the expression.
\frac{\left(n-3\right)\left(n+2\right)}{\left(n^{2}+6n+8\right)\left(n+1\right)}
Divide \frac{n-3}{n^{2}+6n+8} by \frac{n+1}{n+2} by multiplying \frac{n-3}{n^{2}+6n+8} by the reciprocal of \frac{n+1}{n+2}.
\frac{\left(n-3\right)\left(n+2\right)}{\left(n+1\right)\left(n+2\right)\left(n+4\right)}
Factor the expressions that are not already factored.
\frac{n-3}{\left(n+1\right)\left(n+4\right)}
Cancel out n+2 in both numerator and denominator.
\frac{n-3}{n^{2}+5n+4}
Expand the expression.