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