Answer
$\dfrac{3}{5x(x-2)}, x\ne-2, 0, 2$
Work Step by Step
Note that:
$\dfrac{3x+6}{5x^2}\cdot \dfrac{x}{x^2-4}=\dfrac{3x+6}{5x^2}\cdot \dfrac{x}{x^2-2^2}$
Factor each expression completely:
[use special formula $a^2-b^2=(a+b)(a-b)$].
$=\dfrac{3(x+2)}{5x^2}\cdot \dfrac{x}{(x+2)(x-2)}$
Cancel common factors $x+2$ and $x$ to obtain:
$=\dfrac{3}{5x(x-2)}, \space x\ne0, -2, 2$
Hence, the lowest term is $\dfrac{3}{5x(x-2)}, \space x\ne-2, 0, 2$.
