Solve: 1/x-8-1=7/x-8
 a
2
 b
8
 c
no solution
 d
1

Let's solve the equation step by step:

Given the equation:

\[
\frac{1}{x-8} - 1 = \frac{7}{x-8}
\]

1. **Eliminate the fractions**: To eliminate the fractions, multiply both sides by \(x - 8\) (assuming \(x \neq 8\)).

\[
(x - 8) \cdot \left(\frac{1}{x-8} - 1\right) = (x - 8) \cdot \frac{7}{x-8}
\]

This simplifies to:

\[
1 - (x - 8) = 7
\]

2. **Simplify the equation**:

\[
1 - x + 8 = 7
\]

Combine like terms:

\[
9 - x = 7
\]

3. **Solve for \(x\)**:

Subtract 9 from both sides:

\[
-x = 7 - 9
\]

\[
-x = -2
\]

Multiply both sides by \(-1\):

\[
x = 2
\]

4. **Check the solution**: Substitute \(x = 2\) back into the original equation to ensure it is not an extraneous solution.

Substitute \(x = 2\) into the original equation:

\[
\frac{1}{2 - 8} - 1 = \frac{7}{2 - 8}
\]

This simplifies to:

\[
\frac{1}{-6} - 1 = \frac{7}{-6}
\]

Simplifying both sides:

\[
-\frac{1}{6} - \frac{6}{6} = -\frac{7}{6}
\]

\[
-\frac{7}{6} = -\frac{7}{6}
\]

Since both sides are equal, the solution \(x = 2\) is correct.

### Final Answer:
- The correct answer is **(a) 2**.

---

Would you like more details or have any questions?

Here are some related questions:

1. How do you solve equations with variables on both sides?
2. What are extraneous solutions and how do they arise?
3. How do you check if a solution is correct for a given equation?
4. What does it mean when an equation has no solution?
5. How do you handle equations involving fractions?
6. Can all equations be solved algebraically?
7. What is the process of isolating the variable in an equation?
8. How can you use substitution to verify solutions?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation 1/(x-8) - 1 = 7/(x-8) step-by-step. This problem involves eliminating fractions, simplifying equations, and verifying solutions. Suitable for high school students learning algebraic equations.

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