1. **Problem:** Find the domain of the function $$f(x) = \frac{1}{x^2 - 5x + 6}$$. 2. **Formula and rules:** The domain of a function with a denominator is all real numbers except where the denominator is zero because division by zero is undefined. 3. **Find where the denominator is zero:** $$x^2 - 5x + 6 = 0$$ 4. **Factor the quadratic:** $$ (x - 2)(x - 3) = 0 $$ 5. **Solve for x:** $$ x - 2 = 0 \Rightarrow x = 2 $$ $$ x - 3 = 0 \Rightarrow x = 3 $$ 6. **Domain:** All real numbers except $$x = 2$$ and $$x = 3$$. **Final answer:** $$ \text{Domain} = (-\infty, 2) \cup (2, 3) \cup (3, \infty) $$