Steps for Simplifying Algebraic Fractions

for five marks. Hello. Simplify the following. Okay. So when you look at this, you can just remember the following steps. Make sure that all of the bottom parts, or let's first talk about the absolute basics. If I'd said one over three plus one over five, what would you do? Well, well done if you said you would get a common denominator. Whenever you plus and minus fractions, you need to get a common denominator. So that's So that's an important step. We need to get a lowest common denominator. But to get your denominators, you have to make sure that they are all factorized. So this one can be factorized, and this is a trinomial, so that can be factorized. So that'll be our first step. Let's just go factorize. Because if we don't, then you're going to tell me, oh, these two parts are completely different. But maybe they're not. If you factorize this, maybe it ends up looking very similar to that. Okay? So... x plus 7. Now if you factorize this as a trinomial, so let's factorize that over here together. So we look at the number 6. Now we know that the number 6 can be written as 2 times 3, or 1 times 6. Now which one should we choose? Should we choose the 1 and the 6, or should we choose the 2 and the 3? Well how do we work this out? What we do is we look at this term here in the middle with the x, and we try to make minus 1. So you cannot make minus one using these two numbers. Like six minus one is five. One minus six is negative five. One plus six is seven. You're not gonna be able to do it. So it's not that one. So we're gonna use these two. How do you make minus one? Well, you say two minus three, because that gives you minus one. So we're gonna open up two brackets, okay? And we're gonna say x and x. And then we're gonna say positive two for this one, because it's positive in the front. And then negative three. and that is how you factorize that part okay look at that x minus three x minus three oh something similar okay now we're just gonna leave this part because this is already factorized okay now here you can take out a common factor a lot of learners forget about that and look at that x plus two x plus two hashtag just saying so you guys must look out for that okay now to find your lowest common denominator all you do is you just take all the different parts so there's a x plus two we've got one of those so that takes care of that and that there's a x minus three that takes care of that and that and then there's this random two which i'll just put in the front and that takes care of that okay so we've taken care of everything so now what you do okay in the next step you need to make all of these denominators Exactly the same as that. So what that means is the following It means that for this part here if you look at this part, what is it missing? Well, it's missing the two So all we'll do is we will put the two there by multiplying and then what you do to the bottom you have to do To the top here you see how I put a bracket Because if I just put a two there then you would only be giving it to the X. What about the seven bro? You've got to be fair, so you've got to put it in a bracket, so that in the next step, we will give it to both. Okay, excellent. Now we look at this part. Now look at this. What is it missing? Well, it's missing the 2, and it's missing an x plus 2. So what we'll then do, is we'll give it the 2, and we'll give it the x plus 2. Okay, see how I used brackets? Because if I didn't, things look really awkward. Like, what is that, bro? Come on. So you've got to do that, and you've got to do that. Now what you do to the bottom, you must do to the top. So we're going to give it a 2, put a bracket, otherwise you're going to think it says 23, and then we're also going to give it the x plus 2. Okay, now we look at this last part. What is it missing if you look at this part? Well, it's got the 2, and it's got the x plus 2, but it doesn't have the x minus 3. So we'll just give it the x minus 3. What you do to the bottom, you do to the top. And there we go. Now, what we are going to do is we're just going to put one long line, okay? And you're going to put the bottom part like that. But we're not going to multiply the bottom part out. It's weird, right? I know that when you simplify, you're supposed to get rid of brackets, but not in the denominator. For some reason, we, as mathematicians, they love to keep the denominator in the... factorized form like that. But at the top, I just want you to go write everything out now. Please don't multiply anything together yet. It's going to cause some issues, trust me. So then what you do is you just say minus, and then you just say 2 times 3 times x plus 2, and you just say plus. There we go. Now at the top, we have some work to do. We have to go get rid of all the brackets at the top. Okay, so... at the bottom we just keep it as it is okay i hope i have space so you're going to multiply this 2 into this bracket so that's going to become 2x plus 14. all right my apologies i had to go make a bit of space so i erased the one step um and now i've got this okay so that means we have 2x plus 2 and x minus 3. okay so as i said we're going to multiply the 2 into that bracket so you become 2x plus 14. now here just put these two together. So that'll just be negative six, and then x plus two, and then multiply this out. So that'll become two x minus six. Let's quickly do the step over here. So minus six times x is going to be negative six x, and then minus six times positive two is going to be minus 12. So minus six x minus 12 minus six will give minus six x minus 12. And there we go. Okay. Now at the top, you're just going to put all the like terms together. So you've got an x, another one, so that's 2 minus 6 plus 2. So 2 minus 6 is minus 4, minus 4 plus 2 is minus 2. Let's actually just write the answer here. What did we say? Minus 2. And then we have 14 minus 12, which is 2. And then 2 minus 6 is minus 4. And then at the bottom here, you are going to do this. Okay, now you just need to do another little check at the top to make sure we can maybe factorize further. And in fact, we can. We can take out a negative 2, and then you'd be left with x plus 2. How did I do that? We'll check here. If you multiply these two together, what do you get? Negative 2x. And if you multiply these two together, you get negative 4, which is what we had. Now the reason I did that is because if you now look at the bottom, we have things that can cancel out. So here we're going to have those cancel out, and the 2s can also cancel out. And so for our final answer, you're going to have minus 1 at the top, because there's nothing there except the little negative. And then at the bottom, you're going to be left with x minus 3. And that is our final answer.

for five marks. Hello. Simplify the following.

Okay. So when you look at this, you can just remember the following steps. Make sure that all of the bottom parts, or let's first talk about the absolute basics. If I'd said one over three plus one over five, what would you do?

Well, well done if you said you would get a common denominator. Whenever you plus and minus fractions, you need to get a common denominator. So that's So that's an important step.

We need to get a lowest common denominator. But to get your denominators, you have to make sure that they are all factorized. So this one can be factorized, and this is a trinomial, so that can be factorized. So that'll be our first step.

Let's just go factorize. Because if we don't, then you're going to tell me, oh, these two parts are completely different. But maybe they're not. If you factorize this, maybe it ends up looking very similar to that. Okay?

So... x plus 7. Now if you factorize this as a trinomial, so let's factorize that over here together. So we look at the number 6. Now we know that the number 6 can be written as 2 times 3, or 1 times 6. Now which one should we choose?

Should we choose the 1 and the 6, or should we choose the 2 and the 3? Well how do we work this out? What we do is we look at this term here in the middle with the x, and we try to make minus 1. So you cannot make minus one using these two numbers. Like six minus one is five. One minus six is negative five.

One plus six is seven. You're not gonna be able to do it. So it's not that one.

So we're gonna use these two. How do you make minus one? Well, you say two minus three, because that gives you minus one. So we're gonna open up two brackets, okay? And we're gonna say x and x.

And then we're gonna say positive two for this one, because it's positive in the front. And then negative three. and that is how you factorize that part okay look at that x minus three x minus three oh something similar okay now we're just gonna leave this part because this is already factorized okay now here you can take out a common factor a lot of learners forget about that and look at that x plus two x plus two hashtag just saying so you guys must look out for that okay now to find your lowest common denominator all you do is you just take all the different parts so there's a x plus two we've got one of those so that takes care of that and that there's a x minus three that takes care of that and that and then there's this random two which i'll just put in the front and that takes care of that okay so we've taken care of everything so now what you do okay in the next step you need to make all of these denominators Exactly the same as that. So what that means is the following It means that for this part here if you look at this part, what is it missing? Well, it's missing the two So all we'll do is we will put the two there by multiplying and then what you do to the bottom you have to do To the top here you see how I put a bracket Because if I just put a two there then you would only be giving it to the X.

What about the seven bro? You've got to be fair, so you've got to put it in a bracket, so that in the next step, we will give it to both. Okay, excellent. Now we look at this part.

Now look at this. What is it missing? Well, it's missing the 2, and it's missing an x plus 2. So what we'll then do, is we'll give it the 2, and we'll give it the x plus 2. Okay, see how I used brackets? Because if I didn't, things look really awkward. Like, what is that, bro?

Come on. So you've got to do that, and you've got to do that. Now what you do to the bottom, you must do to the top. So we're going to give it a 2, put a bracket, otherwise you're going to think it says 23, and then we're also going to give it the x plus 2. Okay, now we look at this last part.

What is it missing if you look at this part? Well, it's got the 2, and it's got the x plus 2, but it doesn't have the x minus 3. So we'll just give it the x minus 3. What you do to the bottom, you do to the top. And there we go.

Now, what we are going to do is we're just going to put one long line, okay? And you're going to put the bottom part like that. But we're not going to multiply the bottom part out.

It's weird, right? I know that when you simplify, you're supposed to get rid of brackets, but not in the denominator. For some reason, we, as mathematicians, they love to keep the denominator in the... factorized form like that.

But at the top, I just want you to go write everything out now. Please don't multiply anything together yet. It's going to cause some issues, trust me. So then what you do is you just say minus, and then you just say 2 times 3 times x plus 2, and you just say plus. There we go.

Now at the top, we have some work to do. We have to go get rid of all the brackets at the top. Okay, so... at the bottom we just keep it as it is okay i hope i have space so you're going to multiply this 2 into this bracket so that's going to become 2x plus 14. all right my apologies i had to go make a bit of space so i erased the one step um and now i've got this okay so that means we have 2x plus 2 and x minus 3. okay so as i said we're going to multiply the 2 into that bracket so you become 2x plus 14. now here just put these two together.

So that'll just be negative six, and then x plus two, and then multiply this out. So that'll become two x minus six. Let's quickly do the step over here. So minus six times x is going to be negative six x, and then minus six times positive two is going to be minus 12. So minus six x minus 12 minus six will give minus six x minus 12. And there we go. Okay.

Now at the top, you're just going to put all the like terms together. So you've got an x, another one, so that's 2 minus 6 plus 2. So 2 minus 6 is minus 4, minus 4 plus 2 is minus 2. Let's actually just write the answer here. What did we say?

Minus 2. And then we have 14 minus 12, which is 2. And then 2 minus 6 is minus 4. And then at the bottom here, you are going to do this. Okay, now you just need to do another little check at the top to make sure we can maybe factorize further. And in fact, we can. We can take out a negative 2, and then you'd be left with x plus 2. How did I do that? We'll check here.

If you multiply these two together, what do you get? Negative 2x. And if you multiply these two together, you get negative 4, which is what we had.

Now the reason I did that is because if you now look at the bottom, we have things that can cancel out. So here we're going to have those cancel out, and the 2s can also cancel out. And so for our final answer, you're going to have minus 1 at the top, because there's nothing there except the little negative. And then at the bottom, you're going to be left with x minus 3. And that is our final answer.

Transcript for:Steps for Simplifying Algebraic Fractions

Transcript for:
Steps for Simplifying Algebraic Fractions