O Merge $19 \mathrm{Z3} 19 \mathrm{Z4}$ Mark Kassis 07/05/23 5:19 PM The following rational equation has denominators that contain variables. For this 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. \[ \frac{8 x}{x+1}=4-\frac{8}{x+1} \] a. What are the value or values of the variable that makes the denominators zero? \[ x= \] (Simplify your answer. Use a comma to separate answers as needed.) b. Solve the equation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \{\} (Type an integer or a simplified fraction. 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 $\varnothing$. This quiz: 48 point(s) possible This question: 5 point(s) possible Submit qu Submit qu
Solution
Step 1 ：The first part of the question asks for the values of x that make the denominator zero. Looking at the equation, we can see that the denominator is x+1. Therefore, the value of x that makes the denominator zero is -1.
Step 2 ：For the second part of the question, we need to solve the equation. We can start by combining the two fractions on either side of the equation. This will give us a single fraction on each side. We can then cross-multiply to get rid of the fractions and solve for x.
Step 3 ：The solution to the equation is an empty set. This means that there are no real values of x that satisfy the equation. Therefore, the solution set is \(\varnothing\).
Step 4 ：Final Answer: a. The value of the variable that makes the denominators zero is \(\boxed{-1}\). b. The solution set is \(\boxed{\varnothing}\).
