The equation `|x|+|x/(x-1)|=x^(2)/(|x-1|)` is always true for x belongs to A) {0}U`(1,infty)` , B) `(1, infty)`, C) `(-1,1)`, D) `(-infty,infty)`

Explanation

To solve the equation \( |x| + \left| \frac{x}{x-1} \right| = \frac{x^2}{|x-1|} \) and determine the values of \( x \) for which it holds true, we can follow these steps:

### Step 1: Analyze the equation
We start with the equation:
\[ |x| + \left| \frac{x}{x-1} \right| = \frac{x^2}{|x-1|} \]
We need to consider the cases based on the values of \( x \) that affect the absolute values.
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