Answer
0
Work Step by Step
$|x|=\left\{\begin{array}{lll}
x & if & x \geq 0\\
-x & if & x < 0
\end{array}\right.$
Approaching $x=0$ from the right, means $x > 0$...
so,
$\displaystyle \lim_{x\rightarrow 0+}(\frac{1}{x}-\frac{1}{|x|})=\lim_{x\rightarrow 0+}(\frac{1}{x}-\frac{1}{x})=\lim_{x\rightarrow 0+}0=0$.
