List the critical values of the related function. Then solve the inequality.
$$x-6>\frac{2}{x}$$
The critical value(s) is/are
(Simplify your answer. Type an integer or a simplified fraction. Type an exact answer, usin

Step 1 ：The critical values of a function are the x-values where the function is either undefined or its derivative is zero. In this case, the function is undefined when x = 0, so 0 is a critical value.

Step 2 ：To find the other critical values, we need to solve the equation $x-6=\frac{2}{x}$.

Step 3 ：To solve the inequality $x-6>\frac{2}{x}$, we need to find the x-values where the function $x-6-\frac{2}{x}$ is greater than zero.

Step 4 ：The critical values are $3-\sqrt{11}$ and $3+\sqrt{11}$.

Step 5 ：The solution to the inequality is $x>3+\sqrt{11}$ or $0<x<3-\sqrt{11}$.

Step 6 ：Final Answer: The critical values are $\boxed{{\displaystyle 3-\sqrt{11}}}$ and $\boxed{{\displaystyle 3+\sqrt{11}}}$. The solution to the inequality is $x>\boxed{{\displaystyle 3+\sqrt{11}}}$ or $0<x<\boxed{{\displaystyle 3-\sqrt{11}}}$.