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. \( \frac{1}{x-2}+5=\frac{9}{x-2} \) One or more solutions: No solution \( > \) Next Question

1. Start with the given equation: \[ \frac{1}{x-2}+5=\frac{9}{x-2} \] 2. Subtract \(\frac{1}{x-2}\) from both sides: \[ 5=\frac{9}{x-2}-\frac{1}{x-2} \] 3. Combine the fractions on the right-hand side: \[ 5=\frac{9-1}{x-2}=\frac{8}{x-2} \] 4. Multiply both sides of the equation by \((x-2)\) to eliminate the denominator (note that \(x \neq 2\)): \[ 5(x-2)=8 \] 5. Expand and solve for \(x\): \[ 5x-10=8 \] 6. Add 10 to both sides: \[ 5x=18 \] 7. Divide both sides by 5: \[ x=\frac{18}{5} \] Thus, the solution is: \[ \frac{18}{5} \]