Please explain me how to evaluate the limit of function (x^2-9)/(x+3), without use of derivatives? x goes to -3

We notice that if we'll replace x by -3, we'll get an
indetermination "0/0" type.

We'll re-write the numerator,
that is a difference of 2 squares, as a product.

lim (x^2 -
9)/(x+3) = lim (x - 3)(x + 3)/(x+3)

We'll reduce the
fraction by (x+3):

lim (x - 3)(x + 3)/(x+3) = lim (x -
3)

We'll replace x by -3:

lim
(x - 3) = -3 - 3 = -6

The value of the limit
is: lim (x^2 - 9)/(x+3) = -6.