## Problem Statement

Calculate the limit of the function:

$\lim _{x \rightarrow-3} \frac{x^{3}+7 x^{2}+15 x+9}{x^{3}+8 x^{2}+21 x+18}$
## Solution

$$
\begin{aligned}
& \lim _{x \rightarrow-3} \frac{x^{3}+7 x^{2}+15 x+9}{x^{3}+8 x^{2}+21 x+18}=\left\{\frac{0}{0}\right\}=\lim _{x \rightarrow-3} \frac{(x+3)\left(x^{2}+4 x+3\right)}{(x+3)\left(x^{2}+5 x+6\right)}= \\
& =\lim _{x \rightarrow-3} \frac{x^{2}+4 x+3}{x^{2}+5 x+6}=\left\{\frac{0}{0}\right\}=\lim _{x \rightarrow-3} \frac{(x+3)(x+1)}{(x+3)(x+2)}= \\
& =\lim _{x \rightarrow-3} \frac{x+1}{x+2}=\frac{-3+1}{-3+2}=\frac{-2}{-1}=2
\end{aligned}
$$

## Problem Kuznetsov Limits 10-30