Evaluate `lim_(x to 2) [(x^(2) - 4)/(2x + 2)]`

Answer

To evaluate the limit \( \lim_{x \to 2} \frac{x^2 - 4}{2x + 2} \), we can follow these steps:

### Step 1: Substitute the value of \( x \)
First, we will substitute \( x = 2 \) directly into the expression:

\[ \frac{2^2 - 4}{2 \cdot 2 + 2} \]

### Step 2: Simplify the expression
Now, calculate the numerator and the denominator separately:

- Numerator:
\[ 2^2 - 4 = 4 - 4 = 0 \]

- Denominator:
\[ 2 \cdot 2 + 2 = 4 + 2 = 6 \]

So, we have:

\[ \frac{0}{6} \]

### Step 3: Evaluate the limit
Since the result is \( \frac{0}{6} \), we find that:

\[ \lim_{x \to 2} \frac{x^2 - 4}{2x + 2} = 0 \]

Thus, the final answer is:

\[ \boxed{0} \]

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