Answer
$x=-2$
Work Step by Step
Recall: $x=a$ is a vertical asymptote of $f(x)$ if $\lim\limits_{x \to a}f(x)=\pm \infty$.
The vertical asymptotes of a rational function can be determined by the zeros of its denominator.
Find the zero(s) of the denominator of $f(x)$:
$2x+4=0$
$2x=-4$
$x=-2$
Now, check the limit of $f(x)$ as $x$ approaches $-2$:
$\lim\limits_{x \to -2}f(x)=\lim\limits_{x \to -2}\frac{x-1}{2x+4}$
$=\lim\limits_{x \to -2}\frac{1}{2}\cdot \left(\frac{x-1}{x+2}\right)$
$=\lim\limits_{x \to -2}\frac{1}{2}\cdot \left(\frac{x+2-3}{x+2}\right)$
$=\lim\limits_{x \to -2}\frac{1}{2}\cdot \left(1-\frac{3}{x+2}\right)$ (Use the properties for limits)
$=\frac{1}{2}\cdot \left(1-\pm \infty \right)$
$=\pm \infty$
Thus, $x=-2$ is the vertical asymptote of $f(x)$.
