Solve the equation: 1) $$\frac{1}{x^2} - \frac{1}{x} - 6 = 0$$

Let's solve the equation step by step: 1. We have the equation $$\frac{1}{x^2} - \frac{1}{x} - 6 = 0$$. To simplify, let's make a substitution: $$t = \frac{1}{x}$$. Then the equation becomes: $$t^2 - t - 6 = 0$$. 2. Now, let's solve the quadratic equation $$t^2 - t - 6 = 0$$. We can factor this quadratic equation as: $$(t - 3)(t + 2) = 0$$. 3. This gives us two possible values for $$t$$: $$t - 3 = 0 \Rightarrow t_1 = 3$$ $$t + 2 = 0 \Rightarrow t_2 = -2$$ 4. Now, let's find the corresponding values for $$x$$ using the substitution $$t = \frac{1}{x}$$: For $$t_1 = 3$$: $$\frac{1}{x} = 3 \Rightarrow x_1 = \frac{1}{3}$$ For $$t_2 = -2$$: $$\frac{1}{x} = -2 \Rightarrow x_2 = -\frac{1}{2}$$ Thus, the solutions for the equation are $$x_1 = \frac{1}{3}$$ and $$x_2 = -\frac{1}{2}$$. Answer: $$x_1 = \frac{1}{3}, x_2 = -\frac{1}{2}$$