https://file.aiquickdraw.com/mathbot/file/1728906172761d7vkqfbg.jpg

The given image shows a multiplication of two rational expressions:

\[
\frac{y^2 + y - 20}{y^2 + 7y + 10} \times \frac{y^2 - y - 6}{y^2 - 3y - 4}
\]

### Steps to solve:

1. **Factor each quadratic expression**:
   - \(y^2 + y - 20\) factors as \((y - 4)(y + 5)\).
   - \(y^2 + 7y + 10\) factors as \((y + 5)(y + 2)\).
   - \(y^2 - y - 6\) factors as \((y - 3)(y + 2)\).
   - \(y^2 - 3y - 4\) factors as \((y - 4)(y + 1)\).

   Thus, the multiplication becomes:

   \[
   \frac{(y - 4)(y + 5)}{(y + 5)(y + 2)} \times \frac{(y - 3)(y + 2)}{(y - 4)(y + 1)}
   \]

2. **Cancel common factors**:
   - \( (y - 4) \) appears in both the numerator and denominator.
   - \( (y + 5) \) appears in both the numerator and denominator.
   - \( (y + 2) \) appears in both the numerator and denominator.

   After canceling, we are left with:

   \[
   \frac{y - 3}{y + 1}
   \]

### Final Answer:
The simplified expression is:

\[
\frac{y - 3}{y + 1}
\]

---

Would you like a detailed explanation of any part of this process or have any further questions?

Here are some follow-up questions you might consider:
1. What are the steps to factor a quadratic expression?
2. Why can terms be canceled in a rational expression?
3. How do you handle rational expressions with undefined values?
4. Can you multiply rational expressions without factoring them?
5. How can we solve equations involving rational expressions?

**Tip**: Always check for restrictions (undefined values) by setting the denominator equal to zero before canceling any terms.

Simplify the following rational expression: (y^2 + y - 20) / (y^2 + 7y + 10) × (y^2 - y - 6) / (y^2 - 3y - 4)

Learn how to simplify the rational expression (y^2 + y - 20) / (y^2 + 7y + 10) × (y^2 - y - 6) / (y^2 - 3y - 4) through factoring quadratics and canceling common terms. Suitable for students in Grades 8-10.

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