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The simplified form of the given expression \(\frac{y^2 + 2y - 3}{-6y^2 + 6}\) is:

\[
\frac{-(y + 3)}{6(y + 1)}
\]

Would you like further details on this simplification, or have any questions?

Here are five questions that extend this topic:

1. How would the expression change if the denominator had an additional term?
2. Can you factorize both the numerator and denominator before simplifying?
3. How would you handle simplifying if there were higher powers of \(y\) in both the numerator and denominator?
4. What happens if the numerator or denominator cannot be factored?
5. How does simplifying affect the domain of the rational expression?

**Tip:** Always check for common factors between the numerator and denominator before simplifying a rational expression!

Simplify the expression \(\frac{y^2 + 2y - 3}{-6y^2 + 6}\).

Learn how to simplify the rational expression \(\frac{y^2 + 2y - 3}{-6y^2 + 6}\). This detailed solution covers factoring quadratics and simplifying rational expressions, ideal for high school students in grades 9-11.

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