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To calculate the limit:

\[
\lim_{x \to 1} \frac{x^2 + 2x - 3}{x - 1}
\]

First, try to simplify the expression by factoring the numerator. 

The numerator \(x^2 + 2x - 3\) can be factored as:

\[
x^2 + 2x - 3 = (x - 1)(x + 3)
\]

Now, substitute this factored form into the limit:

\[
\lim_{x \to 1} \frac{(x - 1)(x + 3)}{x - 1}
\]

Since \(x - 1\) is present in both the numerator and denominator, we can cancel these terms (as long as \(x \neq 1\)):

\[
\lim_{x \to 1} (x + 3)
\]

Now, substitute \(x = 1\) into the remaining expression:

\[
1 + 3 = 4
\]

Thus, the limit is:

\[
\boxed{4}
\]

Let me know if you'd like further clarification on any steps!

Here are five questions that expand on this:

1. What happens if you try to plug \(x = 1\) into the original expression directly?
2. How can factoring help simplify limit problems?
3. What is the difference between indeterminate forms and defined values?
4. How would this limit change if the numerator were different?
5. Can you find other methods to solve this limit besides factoring?

**Tip:** Always check if direct substitution results in an indeterminate form (like \( \frac{0}{0} \)) before trying other techniques such as factoring or L'Hopital's Rule.

Calculate the limit of lim_(x -> 1) (x^2 + 2x - 3)/(x - 1).

Explore the step-by-step process of calculating the limit of (x^2 + 2x - 3)/(x - 1) as x approaches 1 by factorizing the numerator. Understand how algebraic simplification helps resolve indeterminate forms in limit calculations. Suitable for college-level students studying calculus.

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