$$\mid\frac{1}{x}=\frac{1}{c}\mid=\mid\frac{c-x}{xc}\mid=\frac{1}{\left\vert x\right\vert}\cdot\frac{1}{\left\vert c\right\vert}\cdot\left\vert x-c\right\vert$$

The factor $$\frac{1}{\left\vert x\right\vert}$$ is not good if its near 0.