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\frac{\left(2x+6\right)\left(x+2\right)}{\left(5x+10\right)\left(x^{2}+4x+3\right)}
Multiply \frac{2x+6}{5x+10} times \frac{x+2}{x^{2}+4x+3} by multiplying numerator times numerator and denominator times denominator.
\frac{2\left(x+2\right)\left(x+3\right)}{5\left(x+1\right)\left(x+2\right)\left(x+3\right)}
Factor the expressions that are not already factored.
\frac{2}{5\left(x+1\right)}
Cancel out \left(x+2\right)\left(x+3\right) in both numerator and denominator.
\frac{2}{5x+5}
Expand the expression.
\frac{\left(2x+6\right)\left(x+2\right)}{\left(5x+10\right)\left(x^{2}+4x+3\right)}
Multiply \frac{2x+6}{5x+10} times \frac{x+2}{x^{2}+4x+3} by multiplying numerator times numerator and denominator times denominator.
\frac{2\left(x+2\right)\left(x+3\right)}{5\left(x+1\right)\left(x+2\right)\left(x+3\right)}
Factor the expressions that are not already factored.
\frac{2}{5\left(x+1\right)}
Cancel out \left(x+2\right)\left(x+3\right) in both numerator and denominator.
\frac{2}{5x+5}
Expand the expression.