Solve the rational equation. Enter any solution that checks as an integer or reduced fraction. Separate with commas if there is more than one solution. If there are no solutions, click the No Solution button. \( \frac{1}{x+3}+4=\frac{2}{x+3} \) One or more solutions: No solution \( > \) Next Question

1. Start with the given equation: \[ \frac{1}{x+3} + 4 = \frac{2}{x+3} \] 2. Multiply both sides by \(x+3\) (noting that \(x+3 \neq 0\)) to eliminate the fractions: \[ (x+3)\left(\frac{1}{x+3} + 4\right) = (x+3)\left(\frac{2}{x+3}\right) \] 3. Simplify each term: \[ 1 + 4(x+3) = 2 \] 4. Distribute \(4\) in the equation: \[ 1 + 4x + 12 = 2 \] 5. Combine like terms: \[ 4x + 13 = 2 \] 6. Solve for \(x\) by isolating the variable: \[ 4x = 2 - 13 \] \[ 4x = -11 \] \[ x = -\frac{11}{4} \] 7. Verify that \(x+3 \neq 0\): \[ -\frac{11}{4} + 3 = -\frac{11}{4} + \frac{12}{4} = \frac{1}{4} \neq 0 \] The solution is: \[ -\frac{11}{4} \]