Find the range of `f(x)=(x-[x])/(1-[x]+x '),w h e r e[]` represents the greatest integer function.

Explanation

To find the range of the function \( f(x) = \frac{x - [x]}{1 - [x] + x} \), where \([x]\) represents the greatest integer function, we can follow these steps:

### Step 1: Understand the Components of the Function
The function can be rewritten using the fractional part of \( x \). The fractional part of \( x \) is defined as:
\[ \{x\} = x - [x] \]
Thus, we can express \( f(x) \) as:
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