Prove that `f(x)=x(x/(e^(x)-1)+x/2)` is odd function.

Explanation

To prove that the function \( f(x) = x \left( \frac{x}{e^x - 1} + \frac{x}{2} \right) \) is an odd function, we need to show that \( f(-x) = -f(x) \) for all \( x \).

### Step-by-Step Solution:

1. **Define the function**:
\[ f(x) = x \left( \frac{x}{e^x - 1} + \frac{x}{2} \right) \]
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