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\frac{2k^{2}+21k+27}{9k^{2}-33k+28}\times \frac{\left(3k-4\right)\left(3k+4\right)}{\left(2k+3\right)\left(3k+4\right)}
Factor the expressions that are not already factored in \frac{9k^{2}-16}{6k^{2}+17k+12}.
\frac{2k^{2}+21k+27}{9k^{2}-33k+28}\times \frac{3k-4}{2k+3}
Cancel out 3k+4 in both numerator and denominator.
\frac{\left(2k^{2}+21k+27\right)\left(3k-4\right)}{\left(9k^{2}-33k+28\right)\left(2k+3\right)}
Multiply \frac{2k^{2}+21k+27}{9k^{2}-33k+28} times \frac{3k-4}{2k+3} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(3k-4\right)\left(k+9\right)\left(2k+3\right)}{\left(3k-7\right)\left(3k-4\right)\left(2k+3\right)}
Factor the expressions that are not already factored.
\frac{k+9}{3k-7}
Cancel out \left(3k-4\right)\left(2k+3\right) in both numerator and denominator.
\frac{2k^{2}+21k+27}{9k^{2}-33k+28}\times \frac{\left(3k-4\right)\left(3k+4\right)}{\left(2k+3\right)\left(3k+4\right)}
Factor the expressions that are not already factored in \frac{9k^{2}-16}{6k^{2}+17k+12}.
\frac{2k^{2}+21k+27}{9k^{2}-33k+28}\times \frac{3k-4}{2k+3}
Cancel out 3k+4 in both numerator and denominator.
\frac{\left(2k^{2}+21k+27\right)\left(3k-4\right)}{\left(9k^{2}-33k+28\right)\left(2k+3\right)}
Multiply \frac{2k^{2}+21k+27}{9k^{2}-33k+28} times \frac{3k-4}{2k+3} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(3k-4\right)\left(k+9\right)\left(2k+3\right)}{\left(3k-7\right)\left(3k-4\right)\left(2k+3\right)}
Factor the expressions that are not already factored.
\frac{k+9}{3k-7}
Cancel out \left(3k-4\right)\left(2k+3\right) in both numerator and denominator.