To analyze the expression \(-\frac{1}{5x}\), let’s break it down step by step:
1. Understand the components of the expression:
- The numerator is \(-1\).
- The denominator is \(5x\).
2. Construct the fraction:
- We are taking \(-1\) and dividing it by \(5x\).
3. Evaluate the nature of the expression:
- Since \(-1\) is a constant and \(5x\) includes a variable \(x\), this is a rational function. The variable \(x\) is in the denominator.
4. Simplify the expression:
- The given expression is already in its simplest form. There are no like terms or common factors that can further simplify it.
Thus, the given expression simplifies to [tex]\(\boxed{-\frac{1}{5x}}\)[/tex].