Question

find the vertical asymptote.

$y = \frac{6x - 12}{2x + 12}$

$x = ?$

Explanation:

Step1: Recall vertical asymptote rule

For a rational function \( y = \frac{f(x)}{g(x)} \), vertical asymptotes occur where \( g(x) = 0 \) (and \( f(x)
eq 0 \) at those points, but first solve \( g(x)=0 \)).
Here, \( g(x)=2x + 12 \). Set \( 2x + 12 = 0 \).

Step2: Solve for x

Subtract 12 from both sides: \( 2x = -12 \).
Divide by 2: \( x = \frac{-12}{2} = -6 \).

Check if \( f(-6)
eq 0 \): \( f(x)=6x - 12 \), \( f(-6)=6(-6)-12=-36 - 12=-48
eq0 \). So vertical asymptote at \( x = -6 \).

Answer:

\( x = -6 \)