Answer
Domain: All real numbers except $x= -3, x= -1$
Work Step by Step
Given \begin{equation}
g(x)=\frac{x+7}{(x+3)(x+1)}.
\end{equation} The domain of a rational function consists of all real numbers except numbers that makes the denominator equal to zero. We need to set expression of the denominator to zero to find the numbers that make the denominator zero and exclude them from the domain of the function. \begin{equation}
\begin{aligned}
x+3&=0 \\
x+1&= 0\\
\therefore x&=-3\\
x&=-1.
\end{aligned}
\end{equation} $$
\begin{aligned}
\text{Domain: All real numbers except } x= -3,\quad \ x= -1 \\
\end{aligned}
$$ These values of $x$ represent vertical asymptotes because the factor $(x+3)(x+1)$ does not simplify with the numerator. Use your calculator to check the graph.
