Evaluation of Limit:

We are given the expression:

(x^2 - 5x + 6)/(x - 2)

And we are asked to evaluate the limit as x approaches -2.

Factorization:

The first step is to factorize the numerator. We can do this by finding two numbers that multiply to 6 and add to -5. These numbers are -2 and -3. Therefore, we can write:

(x-2)(x-3)/(x-2)

Cancellation:

Now we can cancel out the (x-2) terms from the numerator and denominator. We are left with:

(x-3)

Limit:

Now we can evaluate the limit as x approaches -2. We can simply substitute -2 in place of x in the expression (x-3) to get:

(-2) - 3 = -5

Therefore, the limit as x approaches -2 is -5.

Explanation:

We were given an expression and asked to evaluate the limit as x approaches -2. To do this, we first factorized the numerator using the quadratic formula. We then canceled out the common factor of (x-2) in the numerator and denominator. Finally, we substituted -2 for x in the simplified expression and evaluated the limit. The limit was found to be -5.