Solve the following equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
1 −
81
x2
= 0
x =

We are given the equation:

\[
1 - \frac{81}{x^2} = 0
\]

### Steps to solve:

1. First, isolate the fraction term by subtracting 1 from both sides:

\[
-\frac{81}{x^2} = -1
\]

2. Multiply both sides by \(-1\) to remove the negative signs:

\[
\frac{81}{x^2} = 1
\]

3. Multiply both sides of the equation by \(x^2\) to eliminate the fraction:

\[
81 = x^2
\]

4. Now, solve for \(x\) by taking the square root of both sides:

\[
x = \pm \sqrt{81}
\]

\[
x = \pm 9
\]

Thus, the solution is:

\[
x = 9, -9
\]

### Final Answer:
\[
x = 9, -9
\]

Do you want any details or have any questions?

Here are 5 related questions:
1. What happens if the constant on the right-hand side of the equation is not 1?
2. How do we handle equations involving higher powers of \(x\)?
3. What are the rules for taking the square root of both sides in an equation?
4. How does the presence of fractions affect the solving process of equations?
5. What if the equation had no real solution—how would we know?

**Tip:** Always check for extraneous solutions when dealing with square roots or rational equations!

Solve the following equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 1 − 81/x^2 = 0

Discover how to solve the rational equation 1 − 81/x^2 = 0 with a detailed step-by-step guide. This problem involves algebraic concepts, including rational equations and the square root property. Appropriate for students in Grades 8-10.

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