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The given expression is:

\[
\frac{1}{xy - x^2} - \frac{1}{y^2 - xy}
\]

We will first simplify both denominators to see if any factoring or common terms can help simplify the expression.

### Step 1: Factor the denominators

1. First denominator: \( xy - x^2 \)
   \[
   xy - x^2 = x(y - x)
   \]
   
2. Second denominator: \( y^2 - xy \)
   \[
   y^2 - xy = y(y - x)
   \]

Now the expression becomes:

\[
\frac{1}{x(y - x)} - \frac{1}{y(y - x)}
\]

### Step 2: Combine the fractions
Since both terms have a common denominator of \( (y - x) \), we can combine the fractions:

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

### Step 3: Simplify the result
Now simplify the expression inside the parentheses:

\[
\frac{1}{x} - \frac{1}{y} = \frac{y - x}{xy}
\]

Thus, the entire expression becomes:

\[
\frac{1}{y - x} \cdot \frac{y - x}{xy}
\]

The \( y - x \) terms cancel out, leaving:

\[
\frac{1}{xy}
\]

### Final Answer:
The simplified expression is:

\[
\frac{1}{xy}
\]

Would you like more details on any of the steps?

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Here are 5 related questions for practice:

1. How do you simplify fractions with common denominators?
2. What is the process for factoring polynomials like \(xy - x^2\)?
3. How can you handle subtraction between two algebraic fractions?
4. What is the cancellation property in algebra, and how does it apply to this problem?
5. How can you use the Least Common Denominator (LCD) method for subtraction?

**Tip:** When simplifying algebraic fractions, always look for common factors in the denominators to make combining the terms easier.

Simplify the expression: 1 / (xy - x^2) - 1 / (y^2 - xy).

Learn how to simplify the rational expression 1 / (xy - x^2) - 1 / (y^2 - xy) by factoring both denominators, combining the fractions, and applying the cancellation property. This step-by-step solution is suitable for high school algebra students.

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