# How to rearrange an algebra formula to change the subject

hi in this particular video we've got this equation and we need to make you the subject at the moment the subject is 1 over F so the reciprocal of F these are kind of B a a star grade questions they are a little bit trickier but they are approached in a very similar way in that what we need to do is multiply reciprocals across all the denominators across in order to make this just a little bit easier to deal with so what I'm going to do is I'm going to multiply the whole equation by u times V times F okay now I put that little dot in there it's just exactly the same as writing multiply so let me just write that out again what we'll end up with is u times V times f times 1 over F so on the left hand side I'm going to get you V F divided by F equals u V F divided by u Plus u V F divided by V okay I appreciate that looks a little bit complex but the big benefits of working with fractions is that we can then cancel the fractions down so make them a little bit easier to deal with so this F and this F I can get rid of and this side becomes u times V on this equation here I've got the to use I can get rid of so that becomes V times F and on this equation I've got the V's that I can deal with that becomes u times F okay so that means then that I've got a situation where I've got a value of U times V and the value you times s so I need to get those two together well that's fairly straightforward if I – you F from this side and providing I do it to the other side as well I've got – you f it means that on this side of the equation I get you v minus u F and that equals V F it's then just a case of factorizing this through so I'm going to take out the value of U which means it's u times V minus F equals V F okay and then I'm going to divide through by V minus F so u equals V F divided by V minus F okay appreciate that's probably a little bit tricky to kind of work with but hopefully you can see here what I've done if you're not sure about any of these steps then please do have a look at some of the other videos in the playlist and that will give you a few more examples please do post pin tweet fax no post these this video like the video that I look forward to seeing you inside the next video