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\frac{\left(m+2\right)\left(m+3\right)}{m+3}\times \frac{m}{m^{2}+3m+2}
Factor the expressions that are not already factored in \frac{m^{2}+5m+6}{m+3}.
\left(m+2\right)\times \frac{m}{m^{2}+3m+2}
Cancel out m+3 in both numerator and denominator.
\frac{\left(m+2\right)m}{m^{2}+3m+2}
Express \left(m+2\right)\times \frac{m}{m^{2}+3m+2} as a single fraction.
\frac{m\left(m+2\right)}{\left(m+1\right)\left(m+2\right)}
Factor the expressions that are not already factored.
\frac{m}{m+1}
Cancel out m+2 in both numerator and denominator.
\frac{\left(m+2\right)\left(m+3\right)}{m+3}\times \frac{m}{m^{2}+3m+2}
Factor the expressions that are not already factored in \frac{m^{2}+5m+6}{m+3}.
\left(m+2\right)\times \frac{m}{m^{2}+3m+2}
Cancel out m+3 in both numerator and denominator.
\frac{\left(m+2\right)m}{m^{2}+3m+2}
Express \left(m+2\right)\times \frac{m}{m^{2}+3m+2} as a single fraction.
\frac{m\left(m+2\right)}{\left(m+1\right)\left(m+2\right)}
Factor the expressions that are not already factored.
\frac{m}{m+1}
Cancel out m+2 in both numerator and denominator.