1. We are asked to find the limit: $$\lim_{x \to 2} \frac{x^2 + 4x}{x^2 - 4x}$$ 2. The formula for limits involving rational functions is to first try direct substitution. If it results in an indeterminate form like $\frac{0}{0}$, then factor and simplify. 3. Substitute $x=2$: $$\frac{2^2 + 4(2)}{2^2 - 4(2)} = \frac{4 + 8}{4 - 8} = \frac{12}{-4} = -3$$ 4. Since direct substitution gave a defined value, the limit is: $$\boxed{-3}$$ This means as $x$ approaches 2, the function approaches $-3$.