Keeping the restrictions in mind, solve the equation. \( \frac{3}{x}-\frac{9}{8 x}+3 \) a. What is/are the va ue or values of the variable that make(s) the denominator variables. For x \( =0 \) (Simplify your answer Use a comma to separate answers as needed)

To determine the restrictions for the given expression and identify the values of \( x \) that make the denominators zero, follow these steps: ### Given Expression: \[ \frac{3}{x} - \frac{9}{8x} + 3 \] ### a. Finding the Values that Make the Denominator Zero **Step 1: Identify the Denominators** - The denominators in the expression are \( x \) and \( 8x \). **Step 2: Set Each Denominator Equal to Zero and Solve for \( x \)** 1. For \( x \): \[ x = 0 \] 2. For \( 8x \): \[ 8x = 0 \] \[ x = 0 \] **Step 3: Combine the Solutions** - Both denominators lead to the same value: \[ x = 0 \] ### **Conclusion** The value that makes the denominators zero is: \[ x = 0 \] **Restrictions:** \[ x \neq 0 \] This means that \( x \) cannot be zero in the original expression, as it would make the expression undefined. **Final Answer:** \[ 0 \]