Could you please discuss or provide an online reference/tutorial which teaches how to do division (or multiplication) of summations? For example in this post there is a question about the same issue, but I don't understand it. Here is an example:
$ \sum_{i=1}^{n} x_i $ divide by (or multiply by)$ \sum_{i=1}^{n} x{_i}{^2}$
Thank you in advance.
The final answer on the page you link is correct (for division). It doesn't simplify. Just think about the $n=2$ case. You'd have $$\frac{x+y}{x^2+y^2}.$$ For multiplication, you can write $$\sum_{i=1}^n x_i\sum_{i=1}^n x_i^2=\sum_{i=1}^n\sum_{j=1}^nx_ix_j^2$$ but personally, I think the first first form is "simpler."