Chapter A.5, Problem 13AYU

To determine

To find: Simplify the given in factored form.

Answer to Problem 13AYU

$\frac{3}{5x\left(x-2\right)}$

Explanation of Solution

Given:

$\frac{3x+6 }{5x^2}\cdot \frac{ x}{x^2-4}$

Calculation:

$\frac{3x+6\cdot x}{5x^2\cdot x^2-4}=\frac{3x^2+6 x}{5x^4-20x^2}=\frac{3x\left(x+2\right)}{5x^2\left(x^2-4\right)}=\frac{3x\left(x+2\right)}{5x^2\left(x^2-2^2\right)}=\frac{3x\left(x+2\right)}{5x^2\left(x+2\right)\left(x-2\right)}=\frac{3}{5x\left(x-2\right)}$