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.

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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 $$\{9\}$$.**
The solution set is $$\{9\}$$.

Solve the equation.

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.

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Solve the equation. 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.