For the following equation, $a$. Write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. $b$. Keeping the restrictions in mind, solve the equation. \[ \frac{2}{x+8}-\frac{1}{x-8}=\frac{5 x}{x^{2}-64} \] a. Write the value or values of the variable that make a denominator zero. $x=\square$ (Use a comma to separate answers as needed.) b. What is the solution of the equation? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \{\} . (Use a comma to separate answers as needed.). B. The solution set is $\{x \mid x$ is a real number $\}$. C. The solution set is $\varnothing$

Step 1 ：First, we need to find the values of x that make the denominator zero. These are the values that we cannot use in our solution because they would make the equation undefined. The denominators in this equation are x+8, x-8, and x^2-64. Setting each of these equal to zero and solving for x will give us the restrictions on the variable.

Step 2 ：The restrictions on the variable x are -8 and 8, because these values make the denominators of the fractions in the equation zero. So, the values of the variable that make a denominator zero are \(-8, 8\).

Step 3 ：Next, we need to solve the equation. To do this, we can first find a common denominator for all the terms in the equation. The common denominator would be x^2-64, which is the same as (x+8)(x-8). We can then multiply each term by this common denominator to get rid of the fractions. After simplifying, we should be able to solve for x.

Step 4 ：The solution to the equation is x = -6. However, this value is not a restriction, so it is a valid solution. So, the solution set is \{-6\}.

Step 5 ：Final Answer: a. The values of the variable that make a denominator zero are \(\boxed{-8, 8}\). b. The solution set is \(\boxed{\{-6\}}\).