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

Explanation

To solve the equation \( \left| \frac{x}{x-1} \right| + |x| = \frac{x^2}{|x-1|} \), we will analyze the equation by considering different cases based on the values of \( x \).

### Step 1: Identify critical points
The critical points occur where the expressions inside the absolute values change sign. The critical points for this equation are:
- \( x = 0 \) (where \( |x| \) changes)
- \( x = 1 \) (where \( |x-1| \) changes)

We will consider the intervals determined by these points: \( (-\infty, 0) \), \( [0, 1) \), and \( [1, \infty) \).
...