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The problem asks you to simplify the following complex fraction:

\[
\frac{\frac{-7x}{x^2 + xy}}{\frac{y}{x^2}}
\]

### Step-by-step solution:

1. **Rewrite the complex fraction as a single division problem:**
   \[
   \frac{-7x}{x^2 + xy} \div \frac{y}{x^2}
   \]
   Dividing by a fraction is equivalent to multiplying by its reciprocal:
   \[
   = \frac{-7x}{x^2 + xy} \times \frac{x^2}{y}
   \]

2. **Multiply the numerators and denominators:**
   \[
   = \frac{-7x \cdot x^2}{(x^2 + xy) \cdot y}
   \]
   This gives:
   \[
   = \frac{-7x^3}{y(x^2 + xy)}
   \]

3. **Factor the denominator:**
   \[
   y(x^2 + xy) = yx(x + y)
   \]
   So the fraction becomes:
   \[
   = \frac{-7x^3}{yx(x + y)}
   \]

4. **Simplify the expression:**
   Cancel out one factor of \(x\) from the numerator and denominator:
   \[
   = \frac{-7x^2}{y(x + y)}
   \]

Thus, the simplified expression is:

\[
\frac{-7x^2}{y(x + y)}
\]

---

Would you like more details on any of these steps, or do you have other questions?

### Related Questions:
1. How do you simplify complex fractions in general?
2. What are the key steps in factoring polynomials?
3. How does multiplying and dividing fractions work?
4. What are some techniques for simplifying algebraic expressions?
5. How do you handle common factors when simplifying fractions?

### Tip:
Always check if there are common factors between the numerator and the denominator before multiplying them, to make the simplification easier.

Simplify the following complex fraction: (-7x) / (x^2 + xy) divided by (y) / (x^2)

Learn how to simplify the complex algebraic fraction (-7x) / (x^2 + xy) divided by (y) / (x^2). This step-by-step solution covers key algebraic concepts such as polynomial factoring, the distributive property, and simplifying expressions. Suitable for students in Grades 9-11.

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