Solve $\frac{|x|}{|x-1|}+|x|=\frac{x^2}{|x-1|}$ Solve $\frac{|x|}{|x-1|}+|x|=\frac{x^2}{|x-1|}$.What will be the easiest techique to solve this sum ?
Just wanted to share a special type of equation and the fastest way to solve it.I am not asking for an answer and i have solved it in my answer given below.Thank You for viewing.

Clearly, $x-1\ne0\iff x\ne1$
and $x^2=|x|(1+|x-1|)\ge0\implies x$ is real
So, $x^2=|x^2|\implies |x|(1+|x-1|-|x|)=0$
If $|x|=0, x=0$
Else $1+|x-1|-|x|=0$
We know  for real $y,|y|=+y$ if $y\ge0$ and $-y$ if $y<0$
So, test for $x<0,0\le x<1,x\ge1$
