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.

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UpStudy AI · Accepted Answer

Let's solve the equation:

$$
\frac{x}{x-6} + 5 = \frac{6}{x-6}
$$

**Step 1: Combine the terms over a common denominator.**

$$
\frac{x}{x-6} + 5 = \frac{6}{x-6}
$$

Subtract $$\frac{x}{x-6}$$ from both sides:

$$
5 = \frac{6}{x-6} - \frac{x}{x-6}
$$

Combine the fractions:

$$
5 = \frac{6 - x}{x-6}
$$

**Step 2: Clear the denominator by multiplying both sides by $$x - 6$$.**

$$
5(x - 6) = 6 - x
$$

Expand the left side:

$$
5x - 30 = 6 - x
$$

**Step 3: Solve for $$x$$.**

Add $$x$$ to both sides:

$$
6x - 30 = 6
$$

Add $$30$$ to both sides:

$$
6x = 36
$$

Divide by $$6$$:

$$
x = 6
$$

**Step 4: Check for validity.**

The original equation has denominators $$x - 6$$, so $$x$$ cannot be $$6$$. However, our solution is $$x = 6$$, which is not allowed.

**Conclusion:**

There is no valid solution to the equation.

**Answer:**  
**B. There is no solution.**
There is no solution.

Solve the equation.

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.

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Solve the equation. 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.