Question

multiply the rational expressions. write your answer in simplest form. $\frac{x + 3}{x^{2}+4x + 3}cdot\frac{4x + 4}{4x^{3}}$
$\frac{1}{1}cdot\frac{1}{4x^{3}}=\frac{1}{4x^{3}}$
$\frac{1}{1}cdot\frac{1}{x^{3}}=\frac{1}{x^{3}}$
$\frac{x + 3}{(x + 4)}cdot\frac{4}{4x^{3}}=\frac{4(x + 3)}{4x^{3}(x + 4)}$
$\frac{x + 3}{(x + 4)}cdot\frac{1}{x^{3}}=\frac{(x + 3)}{x^{3}(x + 4)}$
steps: 1. factor all terms 2. reduce common terms 3. multiply & write in simplest factored form

Explanation:

Step1: Factor the expressions

Factor $x^{2}+4x + 3=(x + 1)(x+3)$ and $4x + 4=4(x + 1)$.
So the expression becomes $\frac{x + 3}{(x + 1)(x + 3)}\cdot\frac{4(x + 1)}{4x^{3}}$.

Step2: Cancel out common terms

Cancel out the common terms $(x + 3)$ and $(x + 1)$ and also the common factor 4.
We get $\frac{1}{1}\cdot\frac{1}{x^{3}}$.

Step3: Multiply the remaining terms

$\frac{1}{1}\cdot\frac{1}{x^{3}}=\frac{1}{x^{3}}$.

Answer:

$\frac{1}{x^{3}}$