The problem asks us to find the Least Common Denominator (LCD) of the expressions $\frac{5x}{(5x+6)^3}$ and $\frac{x-3}{(x+3)(5x+6)^2}$.

1. Problem Description

The problem asks us to find the Least Common Denominator (LCD) of the expressions $\frac{5x}{(5x+6)^3}$ and $\frac{x-3}{(x+3)(5x+6)^2}$.

2. Solution Steps

To find the LCD, we need to consider all unique factors in the denominators and take the highest power of each factor.

The denominators are $(5x+6)^3$ and $(x+3)(5x+6)^2$.

The factors are $(5x+6)$ and $(x+3)$.

The highest power of $(5x+6)$ appearing in the denominators is $(5x+6)^3$.

The highest power of $(x+3)$ appearing in the denominators is $(x+3)^1$.

Thus, the LCD is the product of these highest powers: $(5x+6)^3(x+3)$.

3. Final Answer

$(x+3)(5x+6)^3$