How do we divide in algebra?

Can some one explain me how?

So if you are doing (3xy/4y) / (6y/8x) it's just like dividing fractions invert the bottom part and multiply it by the top part

you then get (24yx^2) / (24y^2) or you then can cancel out the 24 on the top and the bottom and get (yx^2) / (y^2)

the reason for the 'invert and multiply' rule/hack is that you can cancel the bottom part of the fraction (6y/8x) by multiplying it by it's inverse (8x/6y) and then you get one on the bottom, but you have to keep the fraction the same so you have to multiply the whole big fraction ((3xy/4y) / (6y/8x)) by ((8x/6y) / (8x/6y)) so you basically just invert the bottom fraction and multiply it to the top fraction.

The answer is 384 so i know iam smart i love math you can ask me okay i love you and you bettert lobe me cac