Question

which example is the proper set - up (the first step) for dividing the rational expressions? $\frac{7x}{x + 3}div\frac{7}{x^{2}-9}$
$\frac{7x}{x + 3}cdot\frac{7}{x^{2}-9}$
$\frac{7x}{x + 3}cdot\frac{x^{2}-9}{7}$
$\frac{x + 3}{7x}cdot\frac{7}{x^{2}-9}$
$\frac{x + 3}{7x}cdot\frac{x^{2}-9}{7}$

Explanation:

Step1: Recall division rule for fractions

To divide two rational - expressions (which are fractions), we multiply the first fraction by the reciprocal of the second fraction. Given $\frac{a}{b}\div\frac{c}{d}$, it is equivalent to $\frac{a}{b}\times\frac{d}{c}$.
For $\frac{7x}{x + 3}\div\frac{7}{x^{2}-9}$, the reciprocal of $\frac{7}{x^{2}-9}$ is $\frac{x^{2}-9}{7}$. So the first - step is $\frac{7x}{x + 3}\times\frac{x^{2}-9}{7}$.

Answer:

$\frac{7x}{x + 3}\cdot\frac{x^{2}-9}{7}$ (the second option in the list)