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