1. **State the problem:** Find the non-permissible values (values of $x$ that make the denominator zero) for the rational expression $$\frac{x^2 + 2}{x^2 - x - 6}$$ 2. **Formula and rule:** A rational expression is undefined where its denominator equals zero. So, solve $$x^2 - x - 6 = 0$$ 3. **Factor the denominator:** $$x^2 - x - 6 = (x - 3)(x + 2)$$ 4. **Find roots:** Set each factor to zero: $$x - 3 = 0 \Rightarrow x = 3$$ $$x + 2 = 0 \Rightarrow x = -2$$ 5. **Conclusion:** The non-permissible values are $$x = 3$$ and $$x = -2$$ because these make the denominator zero and the expression undefined.