use the theorem on limits of rational functions to find the limit. if necessary, state that the limit does…

use the theorem on limits of rational functions to find the limit. if necessary, state that the limit does not exist. $lim_{x\rightarrow - 3}\frac{x^{2}-9}{x + 3}$ select the correct choice below and fill in the answer box within your choice. a. $lim_{x\rightarrow - 3}\frac{x^{2}-9}{x + 3}=$ (simplify your answer.) b. the limit does not exist.

use the theorem on limits of rational functions to find the limit. if necessary, state that the limit does not exist. $lim_{x\rightarrow - 3}\frac{x^{2}-9}{x + 3}$ select the correct choice below and fill in the answer box within your choice. a. $lim_{x\rightarrow - 3}\frac{x^{2}-9}{x + 3}=$ (simplify your answer.) b. the limit does not exist.

Answer

Explanation:

Step1: Factor the numerator

$x^{2}-9=(x + 3)(x - 3)$

Step2: Simplify the function

$\lim_{x\rightarrow - 3}\frac{x^{2}-9}{x + 3}=\lim_{x\rightarrow - 3}\frac{(x + 3)(x - 3)}{x+3}=\lim_{x\rightarrow - 3}(x - 3)$

Step3: Evaluate the limit

$\lim_{x\rightarrow - 3}(x - 3)=-3-3=-6$

Answer:

A. -6