Answer
$(k+1)(3k^2)$
Work Step by Step
The reciprocal of a fraction $\frac{x}{y}$ is $\frac{y}{x}$. Dividing by a fraction is the same as multiplying by that fraction's reciprocal.
First, we have to multiply together the numerators and the denominators:
$\frac{k^2+k}{5k}\div\frac{1}{15k^2} = \frac{k^2+k}{5k}\cdot\frac{15k^2}{1} = \frac{(k^2+k)(15k^2)}{5k}$
Then, we simplify:
$\frac{5k(k+1)(3k^2)}{5k} = \frac{(k+1)(3k^2)}{1} = (k+1)(3k^2)$
We leave this product in factored form
