Question 6, 3.5.23
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ind the vertical asymptotes, if any, and the values of $x$ corresponding to holes, if any, of the graph of the rational function.
\[
h(x)=\frac{x+3}{x(x+5)}
\]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an equation. Use a comma to separate answers as needed.)
A. There are no vertical asymptotes but there is(are) hole(s) corresponding to $\square$.
B. The vertical asymptote(s) is(are) $\square$ and hole(s) corresponding to $\square$.
C. The vertical asymptote(s) is(are) $\square$. There are no holes.
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Step 1 ：The vertical asymptotes of a rational function occur at the values of x that make the denominator equal to zero, as long as they do not also make the numerator equal to zero. If a value of x makes both the numerator and the denominator equal to zero, then the function has a hole at that x-value.

Step 2 ：In this case, the denominator of the function h(x) is \(x(x+5)\), which equals zero when \(x=0\) or \(x=-5\). We need to check whether these values also make the numerator equal to zero.

Step 3 ：The numerator of the function h(x) is \(x+3\), which equals zero when \(x=-3\). This value does not coincide with the values that make the denominator zero, so the function does not have any holes.

Step 4 ：Therefore, the function h(x) has vertical asymptotes at \(x=0\) and \(x=-5\), and no holes.

Step 5 ：\(\boxed{\text{The vertical asymptote(s) is(are) } x=-5 \text{ and } x=0. \text{ There are no holes.}}\)