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:
$$\frac{\left|\frac3{x^3-8}\right|}{\left|\frac1{x-2}\right|}=1$$
$$\left|\frac{3(x-2)}{x^3-8}\right|=1$$
$$\left|\frac {x-2}{x^3-2^3}\right|=\frac13$$

$$\left|\;\frac3{x^3-8}\;\right|=\left|\;\frac1{x-2}\;\right|\iff3|x-2|=|x-2||x^2+2x+4|$$
Now, it obviously has to be $\,x\ne 2\,$ , so...
