`lim_(x to 2) (x^(2) - 4)/(x + 3)` is equal to

Options

A. 0
B. 1
C. `(1)/(5)`
D. `(8)/(5)`

Answer

To solve the limit \( \lim_{x \to 2} \frac{x^2 - 4}{x + 3} \), we can follow these steps:

### Step 1: Substitute \( x = 2 \) into the expression
We start by substituting \( x = 2 \) directly into the limit expression to see if we can find a value.

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

### Step 2: Calculate the numerator and denominator
Now, we calculate the numerator and the denominator separately.

- The numerator:
\[ 2^2 - 4 = 4 - 4 = 0 \]
- The denominator:
\[ 2 + 3 = 5 \]

### Step 3: Evaluate the limit
Now we substitute these values back into the limit expression:

\[ \frac{0}{5} = 0 \]

### Conclusion
Thus, the limit is:

\[ \lim_{x \to 2} \frac{x^2 - 4}{x + 3} = 0 \]