Solve the equation `|x/(x-1)|+|x|=x^2/|x-1|`

Explanation

Let `f(x)=x/(x-1)` and `g(x)=x`
Then `f(x)+g(x)=x/(x-1)+x=(x^(2))/(x-1)`
`:.` The given equation can be reduced in the form
`|f(x)|+|g(x)|=|f(x)+g(x)|`
Hence `f(x).g(x)ge0`
`implies(x^(2))/(x-1)ge0`

From Wavy curve method `x epsilon (1,oo)uu{0}`