You have the equation:

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

Let's solve for \( x \).

### Step 1: Move 1 to the other side of the equation
\[
-\frac{81}{x^2} = -1
\]

### Step 2: Multiply both sides by -1 to simplify
\[
\frac{81}{x^2} = 1
\]

### Step 3: Cross-multiply to solve for \( x^2 \)
\[
81 = x^2
\]

### Step 4: Take the square root of both sides
\[
x = \pm \sqrt{81}
\]

\[
x = \pm 9
\]

So, the solutions are \( x = 9 \) and \( x = -9 \).

Would you like more details on the steps? Do you have any other questions?

Here are 5 related questions you might find helpful:
1. How do we handle equations involving fractions like this one?
2. What is the process for solving quadratic equations?
3. What are the rules for manipulating square roots in equations?
4. What does it mean for a solution to be positive or negative?
5. How can we apply cross-multiplication to more complex equations?

**Tip**: Always double-check your steps by plugging your solution back into the original equation to verify.

Learn how to solve the rational equation 1 - 81 / x^2 = 0 with a detailed step-by-step solution. This problem covers key algebraic concepts such as solving rational equations and using square roots. Suitable for students in Grades 9-10.

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