1. The problem is to simplify and understand the expression $$\frac{2 \left( \frac{2e^{2} - 1}{2ze} + Pn(2e) \right)}{(2e + 1)^{2}}$$ and then plot its curve. 2. The expression involves exponential terms, a function $Pn(2e)$, and algebraic fractions. 3. First, rewrite the numerator by distributing the 2: $$2 \times \frac{2e^{2} - 1}{2ze} + 2 \times Pn(2e) = \frac{2(2e^{2} - 1)}{2ze} + 2 Pn(2e)$$ 4. Simplify the fraction: $$\frac{2(2e^{2} - 1)}{2ze} = \frac{2e^{2} - 1}{ze}$$ 5. So the numerator becomes: $$\frac{2e^{2} - 1}{ze} + 2 Pn(2e)$$ 6. The denominator is: $$(2e + 1)^{2}$$ 7. Therefore, the full expression is: $$\frac{\frac{2e^{2} - 1}{ze} + 2 Pn(2e)}{(2e + 1)^{2}}$$ 8. To plot this curve, we treat $e$ as the variable and $z$ and $Pn(2e)$ as given functions or constants depending on context. 9. The Desmos-compatible function for plotting is: $$y=\frac{\frac{2e^{2} - 1}{ze} + 2 Pn(2e)}{(2e + 1)^{2}}$$ Final simplified expression ready for plotting: $$y=\frac{\frac{2e^{2} - 1}{ze} + 2 Pn(2e)}{(2e + 1)^{2}}$$