3x-7/x+3-4=0

To solve the equation \(\frac{3x - 7}{x + 3} - 4 = 0\), we can follow these steps:

1. Isolate the fraction: \[ \frac{3x - 7}{x + 3} = 4 \]

2. Multiply both sides by \((x + 3)\) to eliminate the fraction (make sure \(x + 3 \neq 0\)): \[ 3x - 7 = 4(x + 3) \]

3. Expand the right side: \[ 3x - 7 = 4x + 12 \]

4. Rearrange the equation to isolate \(x\): \[ 3x - 4x = 12 + 7 \] \[ -x = 19 \] \[ x = -19 \]

5. Check for any restrictions: We must ensure that \(x + 3 \neq 0\). Since \(x = -19\), we find: \[ -19 + 3 = -16 \neq 0 \] Thus, \(x = -19\) is a valid solution.

The solution to the equation is: \[ \boxed{-19} \]