We are given the equation:

\[
\frac{1}{3u} + \frac{1}{u} = -\frac{1}{15}
\]

### Step-by-Step Solution:

1. **Find a common denominator** for the left-hand side. The common denominator between \(3u\) and \(u\) is \(3u\), so we rewrite the equation:
   \[
   \frac{1}{3u} + \frac{3}{3u} = -\frac{1}{15}
   \]
   This simplifies to:
   \[
   \frac{1 + 3}{3u} = -\frac{1}{15}
   \]
   Which simplifies further to:
   \[
   \frac{4}{3u} = -\frac{1}{15}
   \]

2. **Cross-multiply** to eliminate the fractions:
   \[
   4 \cdot 15 = 3u \cdot (-1)
   \]
   Simplifying:
   \[
   60 = -3u
   \]

3. **Solve for \(u\)**:
   \[
   u = \frac{-60}{3} = -20
   \]

Thus, the solution is:

\[
u = -20
\]

Would you like further clarification, or do you have any questions?

### Related Questions:
1. How would the solution change if the equation were \(\frac{1}{2u} + \frac{1}{u} = -\frac{1}{10}\)?
2. How can we solve similar equations when there are more terms with different denominators?
3. What happens if we introduce a quadratic equation into a similar context?
4. How can we solve this type of equation graphically?
5. How does cross-multiplication help in solving fractional equations?

### Tip:
When dealing with fractions in equations, always find a common denominator first to simplify the equation before proceeding.

This detailed step-by-step solution shows how to solve the fractional equation (1/3u) + (1/u) = -1/15 using algebraic techniques, including finding common denominators and applying cross-multiplication. Perfect for students in Grades 8-10 looking to improve their understanding of fractional equations.

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