1. **State the problem:** Factor the expression $$\frac{15x^2}{5xy} + \frac{25x^3}{3xy}$$. 2. **Rewrite each term:** Simplify each fraction by dividing numerator and denominator. $$\frac{15x^2}{5xy} = \frac{\cancel{15}^3 \times x^2}{\cancel{5}^1 \times x y} = 3 \times \frac{x^2}{x y} = 3 \times \frac{\cancel{x} x}{\cancel{x} y} = \frac{3x}{y}$$ $$\frac{25x^3}{3xy}$$ cannot be simplified further because 25 and 3 have no common factors and $x^3$ over $x$ simplifies to $x^{3-1} = x^2$. So, $$\frac{25x^3}{3xy} = \frac{25 x^2}{3 y}$$ 3. **Rewrite the expression:** $$\frac{3x}{y} + \frac{25 x^2}{3 y}$$ 4. **Find common denominator:** The denominators are $y$ and $3y$. The least common denominator is $3y$. Rewrite the first term with denominator $3y$: $$\frac{3x}{y} = \frac{3x \times 3}{y \times 3} = \frac{9x}{3y}$$ 5. **Add the fractions:** $$\frac{9x}{3y} + \frac{25 x^2}{3 y} = \frac{9x + 25 x^2}{3 y}$$ 6. **Factor the numerator:** $$9x + 25 x^2 = x(9 + 25 x)$$ 7. **Final factored form:** $$\frac{x(9 + 25 x)}{3 y}$$ **Answer:** $$\frac{x(9 + 25 x)}{3 y}$$