Question

multiply the rational expressions. write your answer in simplest form. $\frac{x + 2}{3x^{2}}cdot\frac{3x^{3}-15x^{2}}{6x + 12}$
$\frac{1}{1}cdot\frac{(x - 5)}{6}=\frac{x - 5}{6}$
$\frac{1}{1}cdot\frac{(x - 5)}{2}=\frac{x - 5}{2}$
$\frac{1}{1}cdot\frac{(x + 5)}{6}=\frac{x + 5}{6}$
$\frac{1}{1}cdot\frac{(x + 5)}{2}=\frac{x + 5}{2}$
steps: 1. factor all terms 2. reduce common terms 3. multiply & write in simplest factored form

Explanation:

Step1: Factor the expressions

Factor $3x^{3}-15x^{2}=3x^{2}(x - 5)$ and $6x + 12=6(x + 2)$.
The original expression $\frac{x + 2}{3x^{2}}\cdot\frac{3x^{3}-15x^{2}}{6x + 12}$ becomes $\frac{x + 2}{3x^{2}}\cdot\frac{3x^{2}(x - 5)}{6(x + 2)}$.

Step2: Cancel out common terms

Cancel out the common terms $x + 2$ and $3x^{2}$ in the numerator and denominator.
We get $\frac{1}{1}\cdot\frac{x - 5}{6}$.

Step3: Multiply the remaining terms

$\frac{1}{1}\cdot\frac{x - 5}{6}=\frac{x - 5}{6}$.

Answer:

$\frac{x - 5}{6}$