Question

which example is the first step for dividing the rational expressions? $\frac{x + 2}{3x^{2}}div\frac{6x + 12}{3x^{3}-15x^{2}}$ $\frac{x + 2}{3x^{2}}cdot\frac{3x^{3}-15x^{2}}{6x + 12}$ $\frac{3x^{2}}{x + 2}cdot\frac{3x^{3}-15x^{2}}{6x + 12}$ $\frac{x + 2}{3x^{2}}cdot\frac{6x + 12}{3x^{3}-15x^{2}}$ $\frac{3x^{2}}{x + 2}cdot\frac{6x + 12}{3x^{3}-15x^{2}}$

Explanation:

Step1: Recall division - to - multiplication rule

To divide two rational expressions $\frac{a}{b}\div\frac{c}{d}$, we change the division to multiplication and flip the second fraction, getting $\frac{a}{b}\times\frac{d}{c}$. For $\frac{x + 2}{3x^{2}}\div\frac{6x + 12}{3x^{3}-15x^{2}}$, it becomes $\frac{x + 2}{3x^{2}}\times\frac{3x^{3}-15x^{2}}{6x + 12}$.

Answer:

$\frac{x + 2}{3x^{2}}\cdot\frac{3x^{3}-15x^{2}}{6x + 12}$ (first option in the list)