Answer
The limit does not exist.
Work Step by Step
$\lim\limits_{x \to -3^{-}} \frac{x^{2}-3x}{x^{2}-9}$
$x$ | $f(x)$
-3.5 | 7
-3.1 | 31
-3.05 | 61
-3.01 | 301
-3.001 | 3001
-3.0001 | 30001
$\lim\limits_{x \to -3^{-}} f(x) = \infty$
$\lim\limits_{x \to -3^{+}} \frac{x^{2}-3x}{x^{2}-9}$
$x$ | $f(x)$
-2.5 | -5
-2.9 | -29
-2.95 | -59
-2.99 | -299
-2.999 | -2999
-2.9999 | -29999
$\lim\limits_{x \to -3^{+}} f(x) = -\infty$
$\lim\limits_{x \to -3^{+}} f(x) \ne \lim\limits_{x \to -3^{-}} f(x)$
