TITLE: What is $\frac{1}{|{x}|}-\frac{x^2}{|x|^3}$?
QUESTION [8 upvotes]: What's the result of:
$$\frac{1}{|{x}|}-\frac{x^2}{|x|^3}$$
Is it 
$$\frac{1}{|{x}|}-\frac{x^2}{|x|x^2}=\frac{1}{|{x}|}-\frac{1}{|x|}=0$$
or
$$\frac{1}{|{x}|}-\frac{x^2}{|x|^2x}=\frac{1}{|{x}|}-\frac{1}{x}\frac{x^2}{|x|^2}=\frac{1}{|{x}|}-\frac{1}{x}=\left\{\begin{matrix}\frac{2}{x},x<0\\ 0,x>0 \end{matrix}\right.$$

REPLY [2 votes]: As the other answers already told you, the first one is true.
But maybe this way of thinking gives you an intuition: Both terms  $\frac{1}{|x|}$ and $\frac{x²}{|x³|}$ are positive and obviously have the same absolute value, so since there is a minus in between, the result must be zero.