## Algebra 1

$(k+1)(3k^2)$
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