The solution for `2/(x + 3) - 4/(x - 3) = (-6)/(x + 3)` is:

Options

A. `9`
B. `-1`
C. `-3`
D. `3`

Answer

To solve the equation \( \frac{2}{x + 3} - \frac{4}{x - 3} = \frac{-6}{x + 3} \), we will follow these steps:

### Step 1: Move all terms involving \( x \) to one side
We can rearrange the equation to group like terms. We will add \( \frac{4}{x - 3} \) to both sides and add \( \frac{6}{x + 3} \) to both sides:

\[ \frac{2}{x + 3} + \frac{6}{x + 3} = \frac{4}{x - 3} \]

### Step 2: Combine the fractions on the left side
Since both fractions on the left side have the same denominator \( x + 3 \), we can combine them:

\[ \frac{2 + 6}{x + 3} = \frac{4}{x - 3} \]

This simplifies to:

\[ \frac{8}{x + 3} = \frac{4}{x - 3} \]

### Step 3: Cross-multiply
Now, we will cross-multiply to eliminate the fractions:

\[ 8(x - 3) = 4(x + 3) \]

### Step 4: Distribute both sides
Distributing on both sides gives us:

\[ 8x - 24 = 4x + 12 \]

### Step 5: Move all terms involving \( x \) to one side
Now, we will move the \( 4x \) to the left side by subtracting \( 4x \) from both sides:

\[ 8x - 4x - 24 = 12 \]

This simplifies to:

\[ 4x - 24 = 12 \]

### Step 6: Move the constant to the other side
Next, we will add \( 24 \) to both sides to isolate the term with \( x \):

\[ 4x = 12 + 24 \]

This simplifies to:

\[ 4x = 36 \]

### Step 7: Solve for \( x \)
Finally, we will divide both sides by \( 4 \):

\[ x = \frac{36}{4} \]

This simplifies to:

\[ x = 9 \]

### Final Answer
The solution for the equation is \( x = 9 \).

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