1. **State the problem:** Simplify or analyze the expression $$\frac{5x+1}{(2x+1)^2}$$. 2. **Formula and rules:** This is a rational expression where the numerator is a linear polynomial and the denominator is a squared binomial. Important rules include factoring, simplifying by canceling common factors, and understanding the domain (values of $x$ that do not make the denominator zero). 3. **Check for factoring:** The numerator $5x+1$ and denominator $(2x+1)^2$ do not share common factors since $5x+1$ is not a multiple of $2x+1$. 4. **Domain:** The denominator cannot be zero, so solve $2x+1=0$ which gives $x=-\frac{1}{2}$. Thus, $x \neq -\frac{1}{2}$. 5. **Simplification:** Since no common factors exist, the expression is already in simplest form: $$\frac{5x+1}{(2x+1)^2}$$ 6. **Summary:** The expression is simplified as is, with domain restriction $x \neq -\frac{1}{2}$ to avoid division by zero.