The given function is:

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

Let's simplify and analyze it.

### Step 1: Factor the numerator
The numerator \( x^2 + 2x - 3 \) can be factored. We're looking for two numbers that multiply to give \(-3\) and add up to \(2\).

The factors are \((x + 3)(x - 1)\).

Thus, the equation becomes:

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

### Step 2: Identify any simplifications
There are no common factors between the numerator and the denominator, so the expression cannot be simplified further.

### Step 3: Analyze the domain
Since the denominator is \(x + 1\), the function is undefined when \(x = -1\) (division by zero). Therefore, the domain of the function is all real numbers except \(x = -1\).

### Final Form of the Function:
The simplified function is:

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

Would you like a more detailed explanation or graph of this function?

### Related Questions:
1. What is the vertical asymptote of the function?
2. How do you find the horizontal asymptote of a rational function?
3. Can you determine the x-intercepts and y-intercepts of this function?
4. What is the behavior of the function near \(x = -1\)?
5. How does factoring help simplify rational functions?

### Tip:
Always check for restrictions in the domain of rational functions by setting the denominator equal to zero and solving for \(x\).

Discover how to simplify the rational function y = (x^2 + 2x - 3) / (x + 1) by factoring the quadratic numerator and analyzing the domain. This step-by-step guide covers factoring, identifying restrictions in the domain, and understanding rational functions, suitable for Grades 9-12.

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