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We are tasked with evaluating the limit:

\[
\lim_{x \to 3} \frac{x^2 + 4x}{x^2 - 2x - 3}
\]

### Step 1: Check for direct substitution

First, let's substitute \(x = 3\) into the expression:

- Numerator: \(3^2 + 4(3) = 9 + 12 = 21\)
- Denominator: \(3^2 - 2(3) - 3 =

Evaluate the limit: lim(x→3) [(x^2 + 4x) / (x^2 - 2x - 3)]

In this example, we solve the limit lim(x→3) [(x^2 + 4x) / (x^2 - 2x - 3)] by factoring the quadratic expressions. This problem introduces essential concepts of limits, factoring, and algebraic manipulation. Ideal for students in Grades 11-12 studying Precalculus or Calculus.

Math Problem Statement

Solution

Step 1: Check for direct substitution

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