Question

① $\frac{12m^{2}n^{5}}{m + 5}div\frac{3m^{3}n}{m^{2}-25}$

Explanation:

Step1: Recall division - multiplication rule

Dividing by a fraction is multiplying by its reciprocal. So $\frac{12m^{2}n^{5}}{m + 5}\div\frac{3m^{3}n}{m^{2}-25}=\frac{12m^{2}n^{5}}{m + 5}\times\frac{m^{2}-25}{3m^{3}n}$.

Step2: Factor the difference - of - squares

Since $m^{2}-25=(m + 5)(m - 5)$, the expression becomes $\frac{12m^{2}n^{5}}{m + 5}\times\frac{(m + 5)(m - 5)}{3m^{3}n}$.

Step3: Cancel out common factors

Cancel out the common factors $(m + 5)$, and simplify the coefficients and variables. $\frac{12}{3}=4$, $\frac{m^{2}}{m^{3}}=\frac{1}{m}$, $\frac{n^{5}}{n}=n^{4}$. So the result is $4\frac{n^{4}(m - 5)}{m}=\frac{4n^{4}(m - 5)}{m}$.

Answer:

$\frac{4n^{4}(m - 5)}{m}$