Hi guys,

im currently trying to refresh my algebra knowledge as i've been out of school for a while...

I've come across a couple of problems where something is just not clicking, im sure it's very simple but im struggling to understand how the answer has been reached.

the problem im having is with dividing fractions.

I know (4/5) / (6/8) we have to flip the second fraction and then multiply the numerators and multiply the denominators so we get 32/30 or 16/15

I also know that this works when the first term is not a fraction so (s+2) / (6/8) = (s+2) x (8/6) = 8(s+2)/6.

but i get a bit confused when the 2nd term is not a fraction. eg (6/8) / (s+2) i know the answer is 6/8(s+2) by multiplying the denominator and the second term but im not really sure why or how it works?

Do i just need to learn and accept that this is the rule and move on or is there an easy way to understand why this is done that I am not seeing?

The second problem i have is simplifying:

(3/X+2) / (X/2X+4)

Could some one please give me a step by step guide to how this is simplified?

The way I thought this was done is by "flipping" the second fraction and then multiplying both numerators and denominators to get 3(2X+4) / X(X+2) . I know this is wrong the answer is infact 6/X i'm just not really sure how you get there?

Im sure these problems are blatantly obvious to most but its been a while since I last used any algebra and this issue of simplifying equations where fractions are being divided is all that's holding me back at the moment.

I would really appreciate an explanation, thanks guys!