The given expression for \( y \) appears to be:

\[
y = \frac{x^2 + x - 2}{2x^2 + x - 1}
\]

Is this the correct interpretation? If so, here's how you can simplify or analyze this expression:

### 1. Factorization (if possible)

#### Step 1: Factor the numerator and denominator
- **Numerator**: \( x^2 + x - 2 \) can be factored as \( (x - 1)(x + 2) \).
- **Denominator**: \( 2x^2 + x - 1 \) can be factored as \( (2x - 1)(x + 1) \).

So, the expression becomes:

\[
y = \frac{(x - 1)(x + 2)}{(2x - 1)(x + 1)}
\]

#### Step 2: Check for simplifications
There are no common factors between the numerator and denominator, so this is the simplified form.

Would you like to explore further analysis like graphing, finding asymptotes, or critical points?

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### Relative Questions:
1. How would you calculate the roots of the numerator and denominator?
2. What is the domain of this rational function?
3. What are the vertical asymptotes of this function?
4. How can we find the horizontal asymptote for large \(x\)?
5. How would you graph this rational function?

#### Tip: Always check for undefined points by analyzing the denominator, as these will correspond to vertical asymptotes or holes in the graph.

Simplify the rational function y = (x^2 + x - 2) / (2x^2 + x - 1) by factoring the numerator and denominator. Learn key algebraic concepts such as factoring polynomials and simplifying rational expressions, with step-by-step guidance. Suitable for Grades 9-11.

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