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To find the vertical asymptotes and any holes for the function:

\[
h(x) = \frac{x}{x(x+5)}
\]

### Step 1: Identify the Vertical Asymptotes
Vertical asymptotes occur where the denominator is zero, but the numerator is not zero at those points.

1. Set the denominator equal to zero:
   \[
   x(x + 5) = 0
   \]

2. Solve for \( x \):
   \[
   x = 0 \quad \text{or} \quad x = -5
   \]

These values make the denominator zero. Now we need to check the numerator to determine whether they cause asymptotes or holes.

### Step 2: Check for Holes
A hole occurs if a factor in the denominator can also be found in the numerator, allowing it to be canceled out.

In this case, the numerator is simply \( x \), which matches one of the factors in the denominator (\( x \)). This means that at \( x = 0 \), there is a hole rather than a vertical asymptote, as the \( x \) factor cancels out.

### Step 3: Conclusion
- **Vertical Asymptote:** \( x = -5 \)
- **Hole:** \( x = 0 \)

### Final Answer
The correct choice is **B**, with:
- Vertical asymptote at \( x = -5 \)
- Hole at \( x = 0 \)

Would you like more details on any part of the solution? 

Here are some related questions to deepen your understanding:
1. What is the difference between a hole and a vertical asymptote?
2. How do we find horizontal asymptotes of rational functions?
3. How can we determine if a function has an oblique asymptote?
4. What is the effect of holes on the graph of a function?
5. How do we simplify rational functions when identifying holes?

**Tip:** When checking for holes in rational functions, always look for common factors in the numerator and the denominator that can be canceled out.

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the rational function h(x) = x / (x(x+5)).

Learn how to find the vertical asymptotes and holes for the rational function h(x) = x / (x(x+5)). This problem covers key concepts in rational functions, vertical asymptotes, and identifying holes in graphs. Suitable for high school students in Grades 10-12.

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