Let's solve the given mathematical expression step by step.

Given Expression:

$\frac{\frac{xy - y^2}{x - y} - \frac{x^2 - y^2}{xy - y^2}}{\frac{x - y}{x^2 - xy}}$

Step-by-Step Solution:

1. Simplify the numerator: $\frac{xy - y^2}{x - y} - \frac{x^2 - y^2}{xy - y^2}$

2. Simplify the first term: $\frac{xy - y^2}{x - y} = \frac{y(x - y)}{x - y} = y$

3. Simplify the second term: $\frac{x^2 - y^2}{xy - y^2} = \frac{(x - y)(x + y)}{y(x - y)} = \frac{x + y}{y} = \frac{x}{y} + 1$

4. Combine the terms: $y - \left( \frac{x}{y} + 1 \right) = y - \frac{x}{y} - 1$

5. Simplify the numerator: $y - \frac{x}{y} - 1$

6. Simplify the denominator: $\frac{x - y}{x^2 - xy} = \frac{x - y}{x(x - y)} = \frac{1}{x}$

7. Combine the entire expression: $\frac{y - \frac{x}{y} - 1}{\frac{1}{x}}$

8. Simplify the entire expression: $(y - \frac{x}{y} - 1) \cdot x = xy - \frac{x^2}{y} - x$

Thus, the simplified form of the expression is: $xy - \frac{x^2}{y} - x$

If you have any more questions or need further details, feel free to ask!

Here are 5 more questions you might want to consider:

1. How do you solve a system of linear equations using the substitution method?
2. What is the difference between permutations and combinations?
3. How do you determine the limit of a function as it approaches a specific point?
4. What are the steps to solve a differential equation?
5. How do you calculate the area under a curve using integration?

Tip: When simplifying complex fractions, always try to factorize and cancel common terms step by step to make the process easier.