find the product $\frac{8}{6n - 4}cdot(9n^{2}-4)$. an expression can be written in rational form by writing…

find the product $\frac{8}{6n - 4}cdot(9n^{2}-4)$. an expression can be written in rational form by writing it as a fraction with a denominator of

find the product $\frac{8}{6n - 4}cdot(9n^{2}-4)$. an expression can be written in rational form by writing it as a fraction with a denominator of

Answer

Explanation:

Step1: Factor the denominator and the second - factor

Factor $6n - 4=2(3n - 2)$ and $9n^{2}-4=(3n + 2)(3n - 2)$ using the difference - of - squares formula $a^{2}-b^{2}=(a + b)(a - b)$ where $a = 3n$ and $b = 2$. So the expression becomes $\frac{8}{2(3n - 2)}\cdot(3n + 2)(3n - 2)$.

Step2: Simplify the fraction

Cancel out the common factor $(3n - 2)$ and simplify $\frac{8}{2}$. $\frac{8}{2(3n - 2)}\cdot(3n + 2)(3n - 2)=\frac{8}{2}\cdot(3n + 2)$. Since $\frac{8}{2}=4$, the result is $4(3n + 2)=12n+8$.

Answer:

$12n + 8$