Finding the order of a reagent using method of initial rates

[Cameron Sasmor 1G]

When trying to find the order of a reagent in a reaction, I don't understand why you're mathematically allowed to divide one rate formula by another. To me that doesn't seem like that's mathematically allowed. Divided equations by one another isn't something that's allowed in math last time I checked, so I don't know what kind of logical flaw I'm missing here and I'd like some help figuring it out.

[Chem_Mod]

Dividing equations is mathematically allowed as long as we aren't dividing by zero. We assume that our rates and reactants aren't zero so this is okay.

[Neil DSilva 1L]

If you look at page 56 in the course reader at the example problem with and , we divide because we're finding the ratio of Rate 2 to Rate 1 (and this gives allows us to analyze the rates).