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: \[ \boxed{-19} \]