The given expression is \(\frac{a - b}{a + b}\) - \(\frac{a + b}{a - b}\).

To simplify this, we can find a common denominator, which is \((a + b)(a - b)\). This simplifies to \(a^2 - b^2\).

So, the expression becomes:

\(\frac{(a - b)(a - b)}{a^2 - b^2}\) - \(\frac{(a + b)(a + b)}{a^2 - b^2}\)

This simplifies to:

\(\frac{a^2 - 2ab + b^2}{a^2 - b^2}\) - \(\frac{a^2 + 2ab + b^2}{a^2 - b^2}\)

Subtracting these gives:

\(\frac{-4ab}{a^2 - b^2}\)