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\frac{\left(k+2\right)\left(k+6\right)}{\left(k+5\right)\left(k+6\right)}\times \frac{k^{2}+5k}{k^{2}-2k-8}
Factor the expressions that are not already factored in \frac{k^{2}+8k+12}{k^{2}+11k+30}.
\frac{k+2}{k+5}\times \frac{k^{2}+5k}{k^{2}-2k-8}
Cancel out k+6 in both numerator and denominator.
\frac{\left(k+2\right)\left(k^{2}+5k\right)}{\left(k+5\right)\left(k^{2}-2k-8\right)}
Multiply \frac{k+2}{k+5} times \frac{k^{2}+5k}{k^{2}-2k-8} by multiplying numerator times numerator and denominator times denominator.
\frac{k\left(k+2\right)\left(k+5\right)}{\left(k-4\right)\left(k+2\right)\left(k+5\right)}
Factor the expressions that are not already factored.
\frac{k}{k-4}
Cancel out \left(k+2\right)\left(k+5\right) in both numerator and denominator.
\frac{\left(k+2\right)\left(k+6\right)}{\left(k+5\right)\left(k+6\right)}\times \frac{k^{2}+5k}{k^{2}-2k-8}
Factor the expressions that are not already factored in \frac{k^{2}+8k+12}{k^{2}+11k+30}.
\frac{k+2}{k+5}\times \frac{k^{2}+5k}{k^{2}-2k-8}
Cancel out k+6 in both numerator and denominator.
\frac{\left(k+2\right)\left(k^{2}+5k\right)}{\left(k+5\right)\left(k^{2}-2k-8\right)}
Multiply \frac{k+2}{k+5} times \frac{k^{2}+5k}{k^{2}-2k-8} by multiplying numerator times numerator and denominator times denominator.
\frac{k\left(k+2\right)\left(k+5\right)}{\left(k-4\right)\left(k+2\right)\left(k+5\right)}
Factor the expressions that are not already factored.
\frac{k}{k-4}
Cancel out \left(k+2\right)\left(k+5\right) in both numerator and denominator.