Question

multiply the rational expressions. write your answer in simplest form.
\\(\frac{6}{x - 2}\cdot\frac{x^{2}-4}{6x}\\)
\\(\frac{x + 2}{x}\\)
\\(x + 2\\)
\\(\frac{x - 2}{x}\\)
\\(\frac{x + 2}{-x}\\)
steps:

1. factor all terms
2. reduce common terms
3. multiply & write in simplest factored form

Explanation:

Step1: Factor the difference - of - squares

We know that $x^{2}-4=(x + 2)(x - 2)$ by the formula $a^{2}-b^{2}=(a + b)(a - b)$. So the expression becomes $\frac{6}{x - 2}\cdot\frac{(x + 2)(x - 2)}{6x}$.

Step2: Cancel out common terms

Cancel out the common factors. We can cancel out the factor of 6 in the numerator and denominator, and also the factor of $(x - 2)$ in the numerator and denominator. After canceling, we have $\frac{x + 2}{x}$.

Answer:

$\frac{x + 2}{x}$