1. **State the problem:** Simplify the expression $\frac{y}{12x^5} + \frac{5}{9x^2}$. 2. **Find a common denominator:** The denominators are $12x^5$ and $9x^2$. The least common denominator (LCD) is the least common multiple of $12$ and $9$, and the highest power of $x$ present. - $\text{LCM}(12,9) = 36$ - Highest power of $x$ is $x^5$ So, $\text{LCD} = 36x^5$. 3. **Rewrite each fraction with the LCD:** - For $\frac{y}{12x^5}$, multiply numerator and denominator by $\frac{3}{3}$ to get $\frac{3y}{36x^5}$. - For $\frac{5}{9x^2}$, multiply numerator and denominator by $\frac{4x^3}{4x^3}$ to get $\frac{20x^3}{36x^5}$. 4. **Add the fractions:** $$\frac{3y}{36x^5} + \frac{20x^3}{36x^5} = \frac{3y + 20x^3}{36x^5}$$ 5. **Final answer:** $$\boxed{\frac{3y + 20x^3}{36x^5}}$$