https://file.aiquickdraw.com/mathbot/file/1724591777027wm7movgj.jpg

The expression provided in the image is:

\[
\frac{1 - y^2}{y - y^3}
\]

Let's simplify this step by step.

1. **Factor the numerator**:  
   The numerator \( 1 - y^2 \) is a difference of squares, which can be factored as:
   \[
   1 - y^2 = (1 - y)(1 + y)
   \]

2. **Factor the denominator**:  
   The denominator \( y - y^3 \) can be factored by taking out the common factor \( y \):
   \[
   y - y^3 = y(1 - y^2)
   \]
   Since \( 1 - y^2 = (1 - y)(1 + y) \), we can rewrite the denominator as:
   \[
   y(1 - y^2) = y(1 - y)(1 + y)
   \]

3. **Simplify the expression**:  
   Now, substitute the factored forms into the expression:
   \[
   \frac{(1 - y)(1 + y)}{y(1 - y)(1 + y)}
   \]
   Notice that \( (1 - y)(1 + y) \) is present in both the numerator and the denominator. These can be canceled out:
   \[
   \frac{(1 - y)(1 + y)}{y(1 - y)(1 + y)} = \frac{1}{y}
   \]

So, the simplified form of the expression is:

\[
\frac{1}{y}
\]

Would you like more details on this solution, or do you have any questions?

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Here are five related questions you might find helpful:
1. How do you factor other types of polynomial expressions?
2. What is the general formula for the difference of squares?
3. Can all cubic polynomials be factored using simple methods?
4. What are the common factorization techniques for higher-degree polynomials?
5. How does canceling out terms in fractions work, and when is it valid?

**Tip:** Always double-check your factorization and simplifications to ensure that no terms were incorrectly canceled or omitted.

Learn how to simplify the fraction (1 - y^2) / (y - y^3) step-by-step. This problem involves algebraic concepts like polynomials and fraction simplification, focusing on the difference of squares formula. Suitable for high school students.

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