Simplify (x^2 - 9)/(x - 3), where x != 3.

Step 1: Factor the numerator
Recognize x^2 - 9 as a difference of squares:
x^2 - 9 = x^2 - 3^2

Using a^2 - b^2 = (a - b)(a + b): 
x^2 - 9 = (x - 3)(x + 3)

Step 2: Substitute the factorization:
(x^2 - 9)/(x - 3) = ((x - 3)(x + 3))/(x - 3)

Step 3: Cancel the common factor:
Because x != 3, cancel the common factor x - 3:

x + 3