Duplicated from Tonic1/NexusRaven
∣1x=1c∣=∣c−xxc∣=1∣x∣⋅1∣c∣⋅∣x−c∣\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∣x1=c1∣=∣xcc−x∣=∣x∣1⋅∣c∣1⋅∣x−c∣
The factor $$\frac{1}{\left\vert x\right\vert}$$ is not good if its near 0.