https://file.aiquickdraw.com/mathbot/file/17265312759819692zgb6.jpg

The mathematical expression in the image is:

\[
\left( \frac{x^{-1} + y^{-1}}{x^{-1} - y^{-1}} \right)^{-1}
\]

The problem asks for this expression to be rewritten in a form with a positive exponent.

### Step-by-step solution:

1. **Simplify the exponents** inside the fraction. Recall that \( x^{-1} = \frac{1}{x} \) and \( y^{-1} = \frac{1}{y} \). Substituting these into the equation gives:

\[
\frac{x^{-1} + y^{-1}}{x^{-1} - y^{-1}} = \frac{\frac{1}{x} + \frac{1}{y}}{\frac{1}{x} - \frac{1}{y}}
\]

2. **Simplify the numerator and denominator**:
   - For the numerator: \[ \frac{1}{x} + \frac{1}{y} = \frac{y + x}{xy} \]
   - For the denominator: \[ \frac{1}{x} - \frac{1}{y} = \frac{y - x}{xy} \]

So the entire expression becomes:

\[
\frac{\frac{y + x}{xy}}{\frac{y - x}{xy}} = \frac{y + x}{y - x}
\]

3. Now, the expression becomes:

\[
\left( \frac{y + x}{y - x} \right)^{-1}
\]

4. **Apply the negative exponent**: Recall that \( \left( \frac{a}{b} \right)^{-1} = \frac{b}{a} \). Applying this gives:

\[
\frac{y - x}{y + x}
\]

Thus, the final simplified expression with a positive exponent is:

\[
\boxed{\frac{y - x}{y + x}}
\]

---

Would you like further explanation on any part of the process?

### Related Questions:
1. How do you simplify expressions with negative exponents in general?
2. What are the rules for adding and subtracting fractions?
3. How do you convert a negative exponent to a positive one in more complex expressions?
4. Can you explain how to handle variables with exponents in the denominator?
5. What is the general strategy for simplifying algebraic fractions?

### Tip:
Always check for opportunities to factor or cancel terms when simplifying algebraic fractions.

Bentuk \left( \frac{x^{-1} + y^{-1}}{x^{-1} - y^{-1}} \right)^{-1} dalam pangkat positif adalah ...

Learn how to simplify the algebraic expression \left( \frac{x^{-1} + y^{-1}}{x^{-1} - y^{-1}} \right)^{-1} and rewrite it with positive exponents. This problem covers exponent rules and fraction simplification, suitable for Grades 9-12.

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