Solve the equation. \( \frac{x}{x-5}=\frac{5}{x-5}+6 \) Select the correct choice below and, if necessary, fill in the answer box to complele your choice A. The solution set is \( \{? \) - (Simplity your ansmer. Use a comma to separate answers as needed) B. The solution is the errpty set.

Let's solve the equation step by step! Starting with: \[ \frac{x}{x-5} = \frac{5}{x-5} + 6 \] First, eliminate the fractions by multiplying the entire equation by \(x - 5\) (assuming \(x \neq 5\)): \[ x = 5 + 6(x - 5) \] Now, distribute the 6: \[ x = 5 + 6x - 30 \] \[ x = 6x - 25 \] Rearranging gives: \[ x - 6x = -25 \] \[ -5x = -25 \] \[ x = 5 \] However, remember that this would make the denominator in the original equation zero, so \(x = 5\) is not a valid solution. Thus, we conclude that the solution set is the empty set. The solution is: B. The solution is the empty set.