question\ndetermine the limit shown below in simplest form.\n lim_{x\rightarrow - 2}\frac{x^{2}-9x +…

question\ndetermine the limit shown below in simplest form.\n lim_{x\rightarrow - 2}\frac{x^{2}-9x + 18}{x^{2}-9}

question\ndetermine the limit shown below in simplest form.\n lim_{x\rightarrow - 2}\frac{x^{2}-9x + 18}{x^{2}-9}

Answer

Explanation:

Step1: Factor the numerator and denominator

The numerator $x^{2}-9x + 18=(x - 3)(x - 6)$ and the denominator $x^{2}-9=(x + 3)(x - 3)$. So the function becomes $\lim_{x\rightarrow - 2}\frac{(x - 3)(x - 6)}{(x + 3)(x - 3)}$.

Step2: Simplify the function

Cancel out the common factor $(x - 3)$ (since $x\neq3$ as $x\rightarrow - 2$), we get $\lim_{x\rightarrow - 2}\frac{x - 6}{x + 3}$.

Step3: Substitute $x=-2$

Substitute $x=-2$ into $\frac{x - 6}{x + 3}$, we have $\frac{-2-6}{-2 + 3}=\frac{-8}{1}=-8$.

Answer:

$-8$