Confused on what steps make this equality

Question

The solutions manual gives this equality without an explanation (as usual); I've been stuck at this for a good while and don't feel like wasting any more time $$\frac{(n+1)^2}{2^{n+1}}\times\frac{2^n}{n^2}=\left(1+\frac{1}{n}\right)^2\times\frac{1}{2}$$

Answer 1

\begin{align*} \frac{(n+1)^2}{2^{n+1}}\times\frac{2^n}{n^2}&=\frac{1}{2}\times \frac{(n+1)^2}{2^n}\times\frac{2^n}{n^2}\\ &=\frac{1}{2}\times\left(\frac{n+1}{n}\right)^2\\ &=\frac{1}{2}\times\left(1+\frac{1}{n}\right)^2 \end{align*}