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 \(\boxed{3 - \sqrt{11}}\) and \(\boxed{3 + \sqrt{11}}\). The solution to the inequality is \(x > \boxed{3 + \sqrt{11}}\) or \(0 < x < \boxed{3 - \sqrt{11}}\).