Evaluate
\frac{\left(m+2\right)\left(m+7\right)}{m^{2}+9m+4}
Expand
\frac{m^{2}+9m+14}{m^{2}+9m+4}
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\frac{\left(m^{2}+14m+49\right)\left(m^{2}-3m-10\right)}{\left(m^{2}+2m-35\right)\left(m^{2}+9m+4\right)}
Divide \frac{m^{2}+14m+49}{m^{2}+2m-35} by \frac{m^{2}+9m+4}{m^{2}-3m-10} by multiplying \frac{m^{2}+14m+49}{m^{2}+2m-35} by the reciprocal of \frac{m^{2}+9m+4}{m^{2}-3m-10}.
\frac{\left(m-5\right)\left(m+2\right)\left(m+7\right)^{2}}{\left(m-5\right)\left(m+7\right)\left(m-\left(-\frac{1}{2}\sqrt{65}-\frac{9}{2}\right)\right)\left(m-\left(\frac{1}{2}\sqrt{65}-\frac{9}{2}\right)\right)}
Factor the expressions that are not already factored.
\frac{\left(m+2\right)\left(m+7\right)}{\left(m-\left(-\frac{1}{2}\sqrt{65}-\frac{9}{2}\right)\right)\left(m-\left(\frac{1}{2}\sqrt{65}-\frac{9}{2}\right)\right)}
Cancel out \left(m-5\right)\left(m+7\right) in both numerator and denominator.
\frac{m^{2}+9m+14}{m^{2}+9m+4}
Expand the expression.
\frac{\left(m^{2}+14m+49\right)\left(m^{2}-3m-10\right)}{\left(m^{2}+2m-35\right)\left(m^{2}+9m+4\right)}
Divide \frac{m^{2}+14m+49}{m^{2}+2m-35} by \frac{m^{2}+9m+4}{m^{2}-3m-10} by multiplying \frac{m^{2}+14m+49}{m^{2}+2m-35} by the reciprocal of \frac{m^{2}+9m+4}{m^{2}-3m-10}.
\frac{\left(m-5\right)\left(m+2\right)\left(m+7\right)^{2}}{\left(m-5\right)\left(m+7\right)\left(m-\left(-\frac{1}{2}\sqrt{65}-\frac{9}{2}\right)\right)\left(m-\left(\frac{1}{2}\sqrt{65}-\frac{9}{2}\right)\right)}
Factor the expressions that are not already factored.
\frac{\left(m+2\right)\left(m+7\right)}{\left(m-\left(-\frac{1}{2}\sqrt{65}-\frac{9}{2}\right)\right)\left(m-\left(\frac{1}{2}\sqrt{65}-\frac{9}{2}\right)\right)}
Cancel out \left(m-5\right)\left(m+7\right) in both numerator and denominator.
\frac{m^{2}+9m+14}{m^{2}+9m+4}
Expand the expression.
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