To simplify the expression provided in the problem, let's break it down carefully. The expression is:

$\frac{x^2}{(x-y)(x-z)} + \frac{y^2}{(y-z)(y-x)} + \frac{yz}{(z-x)(z-y)}$

The denominators in each term involve the same factors but in different orders, making this a challenging problem. Here’s a step-by-step solution outline:

1. Common Denominator: The common denominator for these terms would be $(x-y)(x-z)(y-z)$.

2. Rewrite Each Fraction with the Common Denominator: Each term should be expressed over the common denominator.

   • For the first term: $\frac{x^2}{(x-y)(x-z)} = \frac{x^2(y-z)}{(x-y)(x-z)(y-z)}$

   • For the second term: $\frac{y^2}{(y-z)(y-x)} = \frac{y^2(x-z)}{(x-y)(y-z)(y-x)}$

   • For the third term: $\frac{yz}{(z-x)(z-y)} = \frac{yz(x-y)}{(x-y)(x-z)(y-z)}$

3. Combine the Terms: Now that each term is over the common denominator $(x-y)(x-z)(y-z)$, add the numerators together.

4. Simplify the Resulting Expression: After combining the terms, simplify the resulting expression in the numerator to match one of the answer choices.

After following these steps, you should find that the simplified form corresponds to one of the answer choices, specifically:

$\boxed{\frac{-x}{z - x}}$

Let me know if you'd like a deeper breakdown or further clarification.

Would you like further details on any step? Here are some questions that might deepen understanding:

1. How is a common denominator chosen for such rational expressions?
2. How do you distribute terms in the numerator to simplify?
3. Why does the term arrangement in the denominator matter?
4. Could you explain alternative approaches to simplifying complex fractions?
5. What role does factoring play in simplifying such expressions?

Tip: Always check if terms can be factored out or simplified before moving to a common denominator in complex fractions.