Answer
Domain: all real numbers except $x=-2$ and $x=-4$
Work Step by Step
Given \begin{equation}
f(x)=\frac{x+2}{x^2+6 x+8}.
\end{equation} We first note that this a rational function and that its domain must exclude the values of $x$ that make the denominator equal to zero. We must find the zeros of the denominator and exclude it from the domain of the function. Set the denominator to zero and solve for $x$.
\begin{equation}
\begin{aligned}
x^2+6 x+8&=0\\
x^2+2x+4x+8&= 0\\
x(x+2)+4(x+2)&=0\\
(x+2)(x+4)&= 0\\
\therefore x&= -2\\
x&= -4.
\end{aligned}
\end{equation} \begin{equation} \text { Domain: } x \text { is all real numbers except } x=-2 \text { and } x=-4.
\end{equation}
