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.

A shortcut formula for such sums is if $|f(x)|+|g(x)|=|f(x)+g(x)|$ then $f(x).g(x)>0$ then $[\frac{x}{x-1}][x]>=0$ which implies $x^2(x-1)>=0$.But $x^2$ is always >=0.Hence $x>1$ is the solution as well as x=0.
