1. **Stating the problem:** We need to find the value of the expression $$\frac{6 + \sqrt{5}}{6 - \sqrt{5}} \times \frac{6 - \sqrt{5}}{6 + \sqrt{5}}$$. 2. **Formula and important rules:** When multiplying two fractions, multiply the numerators together and the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ Also, note that multiplying a fraction by its reciprocal equals 1: $$\frac{x}{y} \times \frac{y}{x} = 1$$ 3. **Intermediate work:** Here, the two fractions are reciprocals of each other: $$\frac{6 + \sqrt{5}}{6 - \sqrt{5}} \times \frac{6 - \sqrt{5}}{6 + \sqrt{5}} = 1$$ 4. **Explanation:** Since the second fraction is the reciprocal of the first, their product is 1. **Final answer:** None of the options a. to e. equals 1, so the value of the expression is simply 1.