find the vertical asymptote.\n\n$$y = \\frac{4x - 12}{x + 2}$$\n\n$$x = ?$$

Explanation:

Step1: Identify the denominator

The given rational function is $y = \frac{4x - 12}{x + 2}$. The denominator is $x + 2$.

Step2: Set the denominator to zero

Vertical asymptotes occur where the denominator is zero and the numerator is non-zero. $$x + 2 = 0$$

Step3: Solve for x

Subtract 2 from both sides of the equation. $$x = -2$$

Step4: Verify the numerator

Check if the numerator $4x - 12$ is non-zero at $x = -2$. $$4(-2) - 12 = -8 - 12 = -20 \neq 0$$

Answer:

x = -2