1. **Stating the problem:** Create a complex equation that simplifies to the result 3. 2. **Choosing a complex equation:** Let's consider the equation $$\frac{2x^2 - 8}{x - 2} = 3$$ and find the value of $x$ that satisfies it. 3. **Simplify the numerator:** Factor the numerator: $$2x^2 - 8 = 2(x^2 - 4) = 2(x - 2)(x + 2)$$ 4. **Rewrite the equation:** $$\frac{2(x - 2)(x + 2)}{x - 2} = 3$$ 5. **Cancel common factors:** $$\frac{2\cancel{(x - 2)}(x + 2)}{\cancel{(x - 2)}} = 3$$ 6. **Simplify:** $$2(x + 2) = 3$$ 7. **Solve for $x$:** $$2x + 4 = 3$$ $$2x = 3 - 4$$ $$2x = -1$$ $$x = \frac{-1}{2}$$ 8. **Check the solution:** Substitute $x = -\frac{1}{2}$ back into the original equation to verify it equals 3. **Final answer:** The complex equation $$\frac{2x^2 - 8}{x - 2} = 3$$ simplifies to 3 when $x = -\frac{1}{2}$.