Answer
$$\frac{m^2+36m+180}{m^2-15m+50}$$
Work Step by Step
Recall, one never divides by a fraction. Rather, if we want to divide by a fraction, we multiply by the reciprocal of the fraction. Recall, the reciprocal of a fraction is that fraction with the numerator and the denominator switched. Thus, we find:
$$ \frac{\left(2m^2+59m-30\right)}{m^2-10m+25}\times \frac{m^2+m-30}{\left(2m^2-21m+10\right)}\\ \frac{\left(2m-1\right)\left(m+30\right)\left(m-5\right)\left(m+6\right)}{\left(m-5\right)^2\left(2m-1\right)\left(m-10\right)}\\ \frac{\left(m+30\right)\left(m+6\right)}{\left(m-5\right)\left(m-10\right)}\\ \frac{m^2+36m+180}{m^2-15m+50}$$
