Hi, so I'm working through some problems and see two apparently contradicting rules for simplifying a 'fraction over a fraction'. Sorry I cannot figure out how to write proper expressions here... I'm just going to type them out as best as I can.

First, there's x/5 over 2. My solution was to move the 2 up to the top and get 2x/5. Book says no, answer is x/10. Apparently, instead of multiplying by 2/2, I must multiply by 1/2. Ok, this makes sense if you plug in x=1, then .2/2 is .1, not .4. And dividing a number by 5 then also by 2 would be the same as dividing by 10. Damn, don't know where I got that idea from.

Along comes another problem, where we have 1/(x+1)/x. Solution? x/(x+1). Wtf? Thought I couldn't do that? But this makes sense by multiplying by x/x. Now, in the first problem, the 'small fraction' is in the top portion of the 'big fraction'. In the this one, it's in the bottom portion. But last I checked PEMDAS, this shouldn't make a freaking difference

Could someone explain the difference here? I'm clearly missing something...

Thank you