Question

find all vertical asymptotes of the following function.
$f(x) = \frac{x^2 - 4}{3x^2 + 6x}$
answer attempt 1 out of 2
no vertical asymptotes
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Explanation:

Step1: Factor numerator and denominator

Numerator: \(x^{2}-4=(x + 2)(x - 2)\)
Denominator: \(3x^{2}+6x=3x(x + 2)\)
So \(f(x)=\frac{(x + 2)(x - 2)}{3x(x + 2)}\)

Step2: Simplify the function

Cancel out the common factor \((x + 2)\) (for \(x
eq - 2\)), we get \(f(x)=\frac{x - 2}{3x}\), \(x
eq - 2\)

Step3: Find the vertical asymptote

Set the denominator of the simplified function equal to zero.
For \(y=\frac{x - 2}{3x}\), set \(3x=0\), then \(x = 0\)

Answer:

\(x = 0\)