Simplify. \[ \frac{z^{2}-4 z+4}{z^{2}-4} \]

First, let's simplify the expression step by step. The given expression is: \[ \frac{z^{2}-4 z+4}{z^{2}-4} \] Looking at the numerator, we can factor it: \[ z^2 - 4z + 4 = (z-2)^2 \] Now, let's look at the denominator: \[ z^2 - 4 = (z-2)(z+2) \] Now, substituting the factored forms back into the expression, we get: \[ \frac{(z-2)^2}{(z-2)(z+2)} \] We can simplify this by canceling out one \((z-2)\) term from the numerator and the denominator, assuming \(z \neq 2\): \[ \frac{(z-2)}{(z+2)} \] Thus, the simplified form of the expression is: \[ \frac{z-2}{z+2} \quad \text{for} \quad z \neq 2 \]