TITLE: Rewriting $\prod_{i=1}^{n}\frac{x_i}{(1+x_i)^2}$ as $\frac{\prod_{i=1}^{n}x_i}{\prod_{i=1}^{n}(1+x_i)^2}$
QUESTION [7 upvotes]: Can we rewrite
$$\prod_{i=1}^{n}\frac{x_i}{(1+x_i)^2}$$
as 
$$\frac{\prod_{i=1}^{n}x_i}{\prod_{i=1}^{n}(1+x_i)^2}$$
?

REPLY [12 votes]: Yes you can because $\frac AB\times\frac CD=\frac{AC}{BD}$.