1. **Problem Statement:** Given the function $f(b) = \frac{b^3 - 3b^2 + 1}{b(1 - b)}$ and the condition $f(x + 3) = \frac{4x + 1}{4x - 1}$, find the value of $f(2)$. 2. **Step 1: Understand the problem.** We need to find $f(2)$ using the given functional equation for $f(x+3)$. This means we can express $f$ in terms of $x$ shifted by 3 and then substitute to find $f(2)$. 3. **Step 2: Express $f(2)$ in terms of $f(x+3)$.** Let $x + 3 = 2$ so that $x = -1$. Then, $$f(2) = f(x + 3) = \frac{4x + 1}{4x - 1} = \frac{4(-1) + 1}{4(-1) - 1} = \frac{-4 + 1}{-4 - 1} = \frac{-3}{-5} = \frac{3}{5}.$$ 4. **Step 3: Final answer.** $$\boxed{f(2) = \frac{3}{5}}.$$