Find the vertical asymptotes, if any, of the graph of the rational function.
\[
h(x)=\frac{x+2}{x^{2}-4}
\]
(A) no vertical asymptote
(B) $x=2, x=-2$
$x=2$
$x=-2$

Answer

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Answer

$\boxed{x=2, x=-2}$ are the vertical asymptotes

Steps

Step 1 ：Find the values of x for which the denominator is equal to zero: $x^2 - 4 = (x - 2)(x + 2)$

Step 2 ：The denominator is zero when $x = 2$ or $x = -2$

Step 3 ：Check if the numerator is also zero at these points: $x + 2$

Step 4 ：The numerator is zero when $x = -2$

Step 5 ：Since the numerator and denominator are both zero at $x = -2$, it is not a vertical asymptote

Step 6 ：$\boxed{x=2, x=-2}$ are the vertical asymptotes