1. **State the problem:** Subtract the expressions $$\frac{-5}{2u} - \frac{7}{6u^2}$$ and simplify the result. 2. **Find a common denominator:** The denominators are $2u$ and $6u^2$. The least common denominator (LCD) is $$6u^2$$ because $6$ is the least common multiple of $2$ and $6$, and $u^2$ is the highest power of $u$. 3. **Rewrite each fraction with the LCD:** $$\frac{-5}{2u} = \frac{-5 \times 3u}{2u \times 3u} = \frac{-15u}{6u^2}$$ $$\frac{7}{6u^2}$$ is already over the LCD. 4. **Subtract the numerators:** $$\frac{-15u}{6u^2} - \frac{7}{6u^2} = \frac{-15u - 7}{6u^2}$$ 5. **Final simplified expression:** $$\boxed{\frac{-15u - 7}{6u^2}}$$ This is the simplified form since the numerator cannot be factored further to cancel with the denominator.