Find all the values of $x \in \mathbb R$ from an equation Find all the values of $x \in \mathbb{R}$ from this inequality:
$$\left|\frac3{x^3-8}\right|=\left|\frac1{x-2}\right|$$
This is my work:
$$\frac{\left|\frac3{x^3-8}\right|}{\left|\frac1{x-2}\right|}=1$$
$$\left|\frac{3(x-2)}{x^3-8}\right|=1$$
$$\left|\frac {x-2}{x^3-2^3}\right|=\frac13$$

HINT:
$x^3-8=x^3-2^3=(x-2)\{x^2+2x+2^2\}=(x-2)\{(x+1)^2+3\}$
So assuming $x-2\ne0,$ we can safely cancel $x-2$  and utilize $|x^2+2x+4|=x^2+2x+4$
