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How to rearrange an algebra formula to change the subject

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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

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