## Simplifying the Expression: (a - 1/a + 1 - a + 1/a - 1) * 2a / (1 - a^2)

Let's break down the simplification of this algebraic expression step by step.

### 1. Combining Like Terms

**Numerator:**The numerator has several terms that can be combined:- (a - a) = 0
- (-1/a + 1/a) = 0
- (1 - 1) = 0

This leaves us with a simplified numerator of **0**.

**Denominator:**The denominator is already in its simplest form:**(1 - a^2)**

### 2. Simplifying the Expression

Since the numerator is 0, the entire expression becomes:

**0 / (1 - a^2) = 0**

### Conclusion

Therefore, the simplified form of the expression (a - 1/a + 1 - a + 1/a - 1) * 2a / (1 - a^2) is **0**.