The expression you've provided is:

\[
\frac{4x}{1 - x}
\]

This is a rational expression where the numerator is \( 4x \) and the denominator is \( 1 - x \).

### Key Points:
1. **Domain**: The expression is undefined when the denominator is equal to zero. Thus, to find the restriction on \( x \), solve:
   \[
   1 - x = 0 \quad \Rightarrow \quad x = 1
   \]
   So, \( x \neq 1 \).

2. **Simplification**: The expression is already in its simplest form, as no further factorization or simplification can be done.

3. **Behavior**:
   - As \( x \to 1 \), the expression tends to infinity, meaning there is a vertical asymptote at \( x = 1 \).
   - For large positive or negative values of \( x \), the expression behaves approximately like \( 4 \), since the term \( 1 - x \) dominates in the denominator as \( x \) grows.

Would you like a more detailed explanation of any part, or have questions about how to graph this expression?

Here are 5 related questions:
1. How do you find the vertical and horizontal asymptotes of a rational function?
2. Can you simplify more complex rational expressions involving polynomials?
3. How do you find the domain of a rational expression?
4. How do rational expressions behave as \( x \to \infty \)?
5. What are the steps to graph a rational function?

**Tip**: Always check the denominator of a rational expression to ensure you're not dividing by zero.

Explore how to solve the rational expression 4x / (1 - x). This problem involves understanding rational expressions, finding domain restrictions, and determining asymptotic behavior. Suitable for students in Grades 9-11.

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