1. **State the problem:** Simplify the rational expression $$\frac{x^2}{(x-5)^2 (x+1)}$$. 2. **Understand the expression:** The numerator is $$x^2$$ and the denominator is the product of $$(x-5)^2$$ and $$(x+1)$$. 3. **Check for common factors:** There are no common factors between the numerator and denominator since the numerator is $$x^2$$ and the denominator factors are $$(x-5)^2$$ and $$(x+1)$$. 4. **Final simplified form:** The expression is already in simplest form: $$\frac{x^2}{(x-5)^2 (x+1)}$$ This expression cannot be simplified further without specific values for $x$. 5. **Important notes:** The domain excludes values that make the denominator zero, so $x \neq 5$ and $x \neq -1$.