Find the value of k, if
`(3x-4)/((x-3)(x+k))=(1)/(x-3)+(2)/(x+k)`

Answer

To find the value of \( k \) in the equation

\[ \frac{3x-4}{(x-3)(x+k)} = \frac{1}{x-3} + \frac{2}{x+k} \]

we will follow these steps:

### Step 1: Combine the Right-Hand Side
To combine the right-hand side, we need a common denominator, which is \((x-3)(x+k)\):

\[ \frac{1}{x-3} + \frac{2}{x+k} = \frac{(x+k) + 2(x-3)}{(x-3)(x+k)} \]

### Step 2: Simplify the Numerator
Now, simplify the numerator:

\[ (x+k) + 2(x-3) = x + k + 2x - 6 = 3x + k - 6 \]

So, we can rewrite the right-hand side as:

\[ \frac{3x + k - 6}{(x-3)(x+k)} \]

### Step 3: Set the Numerators Equal
Now, we can set the numerators equal to each other since the denominators are the same:

\[ 3x - 4 = 3x + k - 6 \]

### Step 4: Solve for \( k \)
Now, we can simplify this equation:

\[ 3x - 4 = 3x + k - 6 \]

Subtract \( 3x \) from both sides:

\[ -4 = k - 6 \]

Now, add 6 to both sides:

\[ k = -4 + 6 \]

Thus,

\[ k = 2 \]

### Conclusion
The value of \( k \) is \( 2 \).

---