Evaluate `lim_(xto2) (x^(2)-5x+6)/(x^(2)-4).`

Explanation

To evaluate the limit \( \lim_{x \to 2} \frac{x^2 - 5x + 6}{x^2 - 4} \), we will follow these steps:

### Step 1: Factor the numerator and the denominator
The numerator is \( x^2 - 5x + 6 \). We can factor this quadratic expression. The roots of the equation \( x^2 - 5x + 6 = 0 \) can be found using the factorization method:
- The factors of 6 that add up to -5 are -2 and -3.
Thus, we can write:
\[
x^2 - 5x + 6 = (x - 2)(x - 3)
...