Solve the equation. \( \frac{x}{x-6}+5=\frac{6}{x-6} \) Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is \( \} \). (Simplify your answer.) B. There is no solution.

To solve the equation \( \frac{x}{x-6}+5=\frac{6}{x-6} \), we can start by getting a common denominator. Rearranging gives us \( \frac{x + 5(x-6)}{x-6} = \frac{6}{x-6} \). Simplifying further, we have \( \frac{x + 5x - 30}{x-6} = \frac{6}{x-6} \), which means \( \frac{6x - 30}{x-6} = \frac{6}{x-6} \). Cross-multiplying results in \( 6x - 30 = 6 \). Thus, \( 6x = 36 \) gives us \( x = 6 \). However, when we substitute \( x = 6 \) back into the original equation, it leads to division by zero (denominator becomes zero), which means \( x = 6 \) is not a valid solution. Therefore, the correct choice is B. There is no solution. If you love thinking about bizarre cases, this situation is quite unique! It's always a good reminder that some equations have boundaries marked by those pesky denominators. It's like riding a roller coaster—make sure the safety bar is secure, or else! Keep an eye out for those vertical asymptotes; they can really throw a wrench in your solving plans.