Question

write the equation of the vertical asymptote(s) of the rational function. $y = \frac{x - 1}{2x + 5}$
$x = 1$
$x = -\frac{5}{2}$
$x = - 1$
$x = \frac{5}{2}$

Explanation:

Step1: Recall vertical - asymptote rule

The vertical asymptote of a rational function $y=\frac{f(x)}{g(x)}$ occurs where $g(x) = 0$.
For $y=\frac{x - 1}{2x+5}$, set the denominator equal to 0: $2x+5 = 0$.

Step2: Solve for x

Subtract 5 from both sides: $2x=-5$.
Then divide both sides by 2: $x =-\frac{5}{2}$.

Answer:

$x =-\frac{5}{2}$