1. **State the problem:** We are given the function $$E(z) = \frac{z^2}{z^2 + 3z + 2}$$ and asked to determine $$E(k)$$ using the matching approach. 2. **Factor the denominator:** The denominator is a quadratic expression. Factor it: $$z^2 + 3z + 2 = (z + 1)(z + 2)$$ 3. **Rewrite the function:** Now the function is $$E(z) = \frac{z^2}{(z + 1)(z + 2)}$$ 4. **Matching approach:** To find $$E(k)$$, substitute $$z = k$$: $$E(k) = \frac{k^2}{(k + 1)(k + 2)}$$ 5. **Simplify if possible:** There are no common factors to cancel, so this is the simplified form. **Final answer:** $$E(k) = \frac{k^2}{(k + 1)(k + 2)}$$