# BRUCHTERME kürzen einfach erklärt – Brüche mit Variablen, Binomische Formeln ausklammern

Apr 04, 2024Hello and welcome to a new video today that is about how to shorten the bruch therme. There is a relatively simple example of this type of task in the front and there are more in the back which we will see together when we look at the first one. Look at the example, then we see that there are numbers at the top and exe and at the bottom there is also a negative sign between these two hot springs here and that tells you, first of all, that you can't cut anything. as it is now, so now it didn't really occur to him to say ah, there's nothing that's gone recently with the x1 because there's a - in the middle up here, the same would be the case if there was a monastery in the middle, then you're not allowed to do anything, the only way something like that would be possible would be here.

Once you're in the middle, you're allowed to cut off parts, but that's not the case here. how do we manage to have a product like that, so they only allow us to cut out products that work by: Excluding things, let's see what parts appear on the front of both thermal baths and that would be, for example, the xx appears here and the ixs appears on the back different, but that's what it comes down to and then there's something in the middle and only then do we need to shorten the escape down here, so that's our goal, but of course we have to do it step by step. it comes out so we don't do anything at the bottom because it's already there twice iks we can shorten it and at the top we would now exclude anything that means a lot it comes out that means it's the two of it doesn't remember anything about the x3 it becomes something square because it comes out a lot and from the second part here is the 3.

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## bruchterme k rzen einfach erkl rt br che mit variablen binomische formeln ausklammern...

Nothing changes, but we write this six in front of the bracket, so everything that is in the bracket is between brackets and now, as I just said, it is actually between everything, which means that now we can underline the ixs with xtra. And in the end all that's left is the -3 square at the top and the 2 at the bottom. Now you can also see if you're down on two, so there's not much left to shorten and then you'd have to see if the two are also on both parts up there. So there is exactly the same principle as the two here and you could exclude them, but they are not in the second part, so there are not two more in the 3 than Tyler, that's why we can't exclude the two here and that's all we could do, this is now a fraction that has been shortened as much as possible.

Of course, it's not always as easy as in the example, but let's take a look at what we have here, which you can also see at the top, and no. That just means that you're not allowed, and I think you got it, you can't shorten this y with the ypsilon or just shorten anything else individually, which means we have to exclude something here too, so it's actually always shortened to exclusion. or the genomic formulas, we can see that in the other examples when you exclude them, you just look at it, so now it's not so you can directly see what could come out of that, but the five are everywhere. for example, and they look good.

So to shorten it, we take out the five times at the top, it's in the five and also in the 10. What do we have up there if we take away the five from the first part, alone? the ixs remains and if we calculate ten times five we are left with the two and the and anyway because we haven't done anything for a while and we do the same thing below and we also take out of the five, then we would have 15 here until the fifth is 3x plan a so to the left and here the five is drawn all the way forward so now all that's left here is the 5 to the five just one and then and now we can shorten it because now there are those in between that means the five with the fifth we shorten it and we'll see what's left if maybe we can get something out of there x2 and remains on the top and 3x pcie grass on the bottom.

The only thing you can get out of things like These are now numbers, but at the top is that 1, so you can't exclude any other numbers anyway and there are no squares here or any other powers of xy. There's really nothing left that can be done here and that would be your completely shortened, okay, so we've really only excluded one number, but that's not always the case, because that's what we see here when we look at the thing, it's overwhelming to the principle, we have to do it. Let's see again what it is. went in there, so up here 4x square - 4, so we can't see 4 appears on both parts, so you could exclude a 4, for example, if that makes sense, you have to see it, but it would be possible here. nothing can be excluded from the mass anymore.

From the 2x2 part you can also exclude a 2. You don't know if that makes sense and here there is also a two in each part. Now the question is of course how do you start excluding Because you have to start somewhere it all seems like you can cut more than just numbers, so we said above that you could exclude those four and below you could also cut two, that is, a 4, but there is nothing square here. in it always, if that is the case that here the four is also a square, then you have something about the square and the square numbers and here there is also a square number and they are connected to a minus, then that is the third genomic formula o You have to make sure you think about this if you travel with Bruch thermal baths because you can easily convert them back using the British formula, so if you remember the formula, hopefully it will say a + b x h - b is itself square - b square and now we have the part here standing there which is our square - b square because the numbers in the square and iks squared with a - connected and now we want to make this part from it, so we basically apply the third genomic formula to the reverse.

We did it? So let's leave everything at the bottom for now. So standing there we said: let's wait and take it out and see what happens above this x3 from behind. I'll copy it and now comes this part, the third biological formula in reverse. it says it from the agreement rat we just need that Now we have to take the root of 42 of the thing there and the root of the square of aix is ex, that's the first part, then it connects with a more or less once again the variant more so we still have to do it, take the root of the four which would be 2, which is the first part of the parenthesis and now we have to multiply it by the same thing but by one, in the middle, so 2x - 2 like this and now Look, aha, look at the parts that are now actually there and only once in the middle, that means we can delete everything, so there really was more to it, that's how it looked at the beginning and that's often the case, which is why that you always first check if the genomic formulas have to be applied somewhere before putting in the individual numbers and now maybe we'll just write what we have there, so there's still this 2x2 and the x3 and at the bottom just the 2 +4 and now we're back to the point where we don't actually have a square.

Right now there's more of a square number down here, yes, but it's connected to a square inch, so no. We can see again if we can now exclude numbers and down here, there's actually a two there and there's also in that part up there. So you can get a 2 over a second, that is, we get the two out of that part so we would still have the two out there, so only in the iks and back from 2 to 21 in the part there you can't do anything anymore, change and we don't take anything out at the bottom, then we would just have the iks and at the back of the 4 to the two is two and the second two now you can't shorten them very much, but if you have to shorten them all the way until you can't shorten them any more, it's just one part and at the top we have Explore science.

And again, something about the square: that always immediately reminds you of the third genomic formula up here, but we have a three-part sum and that's the first dynamic formula because now there's also ex squared, then just ickx and then just one in the back number okay, what can we do above with the first genomic formula if you apply it backwards says yes a + b in parentheses squared is exact +2 rwb squared says so we have to take the root of the first part? that is, from the square meter 96, the root of 19 is 3 if we take the root of nothing square asics and then that is connected to a plus and now we have to take the root of the most back, the root of one is one , then check if it is between part 66 if it is really double the first time the second then two times 3 times one and that is the 66 there is no error because it may not be a real first genomic formula but it is normal for the tasks and now we can do it here Don't use the third genomic formula yet because 18 is not a square number at all and it doesn't work on two here for the moment, but then we can exclude something because the two are in both parts and if we take the two outside, so we would have here from 18 to 2009, the square remains, of course, and back there, from 2 to two is once and now the square has numbers, so we will leave it like this at the top, but down there Now it can be two times, you should also leave it like this down here now it will be the third again.

The bino mixed formula was applied because we have squares -1 squared, so one is also a square number and now we connect the steps of the genomic formula again, which says yes. we have to take the root of the part from there so that it becomes 3x, then there is one more root from there which is one and the same which is simply multiplied again by the same only then it connects with a - and now we can see quite clearly if finally there are the same things at the bottom now we can shorten the top is written twice so that the square of this triangle +1 then we can remove one of them with the one at the bottom and then at the end actually there's just 3x +1 up and down twice 3x - 1 and now the same thing again, you can see there's still some numbers in there that are clipped at the top and bottom.

But here you can see that now it's stuck up there, so as soon as you are one you can't move anymore and so nothing is possible anymore. Alright, so I hope there are some of the types of tasks you're expecting and if you have any questions, let me know in the comments

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