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\frac{\left(m^{2}+3m+2\right)\left(3m+15\right)}{9\left(m+1\right)}
Divide \frac{m^{2}+3m+2}{9} by \frac{m+1}{3m+15} by multiplying \frac{m^{2}+3m+2}{9} by the reciprocal of \frac{m+1}{3m+15}.
\frac{3\left(m+1\right)\left(m+2\right)\left(m+5\right)}{9\left(m+1\right)}
Factor the expressions that are not already factored.
\frac{\left(m+2\right)\left(m+5\right)}{3}
Cancel out 3\left(m+1\right) in both numerator and denominator.
\frac{m^{2}+7m+10}{3}
Expand the expression.
\frac{\left(m^{2}+3m+2\right)\left(3m+15\right)}{9\left(m+1\right)}
Divide \frac{m^{2}+3m+2}{9} by \frac{m+1}{3m+15} by multiplying \frac{m^{2}+3m+2}{9} by the reciprocal of \frac{m+1}{3m+15}.
\frac{3\left(m+1\right)\left(m+2\right)\left(m+5\right)}{9\left(m+1\right)}
Factor the expressions that are not already factored.
\frac{\left(m+2\right)\left(m+5\right)}{3}
Cancel out 3\left(m+1\right) in both numerator and denominator.
\frac{m^{2}+7m+10}{3}
Expand the expression.