Evaluate
\frac{k+7}{\left(k+3\right)\left(k+6\right)}
Expand
\frac{k+7}{\left(k+3\right)\left(k+6\right)}
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\frac{\left(k+7\right)\left(k+2\right)}{\left(k^{2}+5k+6\right)\left(k+6\right)}
Divide \frac{k+7}{k^{2}+5k+6} by \frac{k+6}{k+2} by multiplying \frac{k+7}{k^{2}+5k+6} by the reciprocal of \frac{k+6}{k+2}.
\frac{\left(k+2\right)\left(k+7\right)}{\left(k+2\right)\left(k+3\right)\left(k+6\right)}
Factor the expressions that are not already factored.
\frac{k+7}{\left(k+3\right)\left(k+6\right)}
Cancel out k+2 in both numerator and denominator.
\frac{k+7}{k^{2}+9k+18}
Expand the expression.
\frac{\left(k+7\right)\left(k+2\right)}{\left(k^{2}+5k+6\right)\left(k+6\right)}
Divide \frac{k+7}{k^{2}+5k+6} by \frac{k+6}{k+2} by multiplying \frac{k+7}{k^{2}+5k+6} by the reciprocal of \frac{k+6}{k+2}.
\frac{\left(k+2\right)\left(k+7\right)}{\left(k+2\right)\left(k+3\right)\left(k+6\right)}
Factor the expressions that are not already factored.
\frac{k+7}{\left(k+3\right)\left(k+6\right)}
Cancel out k+2 in both numerator and denominator.
\frac{k+7}{k^{2}+9k+18}
Expand the expression.
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