Hello to everyone out there, I am trying to understand why F distribution and how it’s related to chi-square. Why there are two formulas (with chi-square values devided by their corresponsing degrees of freedom; and the one with variances).

First formula with variances -> https://i.sstatic.net/BHP51hmz.png
Second one with chi-square values -> https://i.sstatic.net/AJfKQfR8.png

I will be so so very glad to get it! Thank you my savior!