Find the vertical asymptotes, if any, of the graph of the rational function.
-$$h ( x ) = \frac { x + 5 } { x ^ { 2 } - 25 }$$
A) $x = 5$
B) $x = - 5$
C) $x = 5 , x = - 5$
D) no vertical asymptote )x

Question

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator of a rational function is zero (and the numerator is not zero at those points). For $h(x) = \frac{x + 5}{x^2 - 25}$, the denominator is $x^2 - 25 = (x + 5)(x - 5)$. Setting this equal to zero gives $x = -5$ and $x = 5$. However, $x = -5$ also makes the numerator zero, which means it's a hole, not an asymptote. Thus, the only vertical asymptote is at $x = 5$.

Find the Vertical Asymptotes, If Any, of the Graph of the Rational