Solve the equation. \( \frac{7}{4 x-1}=\frac{2}{x+1} \) Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is \( \} \). (Simplify your answer.) B. There is no solution.

To solve the equation: \[ \frac{7}{4x - 1} = \frac{2}{x + 1} \] **Step 1: Identify Restrictions** First, ensure that the denominators are not zero: 1. \(4x - 1 \neq 0 \) ⇒ \( x \neq \frac{1}{4} \) 2. \(x + 1 \neq 0 \) ⇒ \( x \neq -1 \) **Step 2: Cross-Multiply** \[ 7(x + 1) = 2(4x - 1) \] **Step 3: Expand and Simplify** \[ 7x + 7 = 8x - 2 \] Subtract \(7x\) from both sides: \[ 7 = x - 2 \] Add 2 to both sides: \[ x = 9 \] **Step 4: Verify the Solution** Ensure \(x = 9\) does not violate any restrictions: - \(9 \neq \frac{1}{4}\) - \(9 \neq -1\) Both conditions are satisfied. **Conclusion:** The solution set is \(\{9\}\). **Answer:** **A. The solution set is \(\{9\}\).**