Algebraic Fractions: Simplify by Factorise

Transcript

Okay, now we’ve got a fraction we want to simplify that fraction. Now if you have something well if you’re adding something on the numerator and adding or subtracting something on the denominator. See if you can factorize anything okay? Factorizing is a good thing to use when you’re trying to simplify fractions, so trying to see if you can factorize the top and the bottom individually, so 10x plus 20y, what’s common there, guys?

Well x and y, they’re different but 10 and 20 isn’t 10 common? So I can make that 10 go out of the bracket and we just have x plus 2y left inside because 20 divided by 10 is 2. That’s how I factorize it. Remember we’ve done a lot of factorizing in the previous section. And x plus 2y there’s nothing common, so we can’t factorize that and guys now compare the numerator and denominator. Is there anything that we can cancel out? Is there anything common sees how x plus 2y is the same as x plus 2y? We can cancel that whole thing out, so the answer is just 10. Well we can’t factorize the denominator because it’s just five but can you guys see if you can factorize the numerator for me? What’s common with g and 50? Isn’t 10 a common factor?

So I’m going to take 10 out, so we just have g minus 5 left because 50 divided by 10 is 5 right? So now 10 and five, can we cancel those at all? Well, then what’s the common factor of ten and five? Five! So five divided by five is just one. And ten divided by five is two. So we just have 2 g minus 5 left and don’t worry about expanding that out just leaves it like that leave it in factorized form. Find how to factorize top and bottom individually. So look at the top. What’s common? What’s the common factor? Two is it?

Two a common factor, so I’m gonna factorize it by two, so eight divided by two is four, so we just have four k left here and six divided by two is three, so that’s how I have that left inside the bracket and four k minus three. there are no common factors so I just leave it as it is and you can see it immediately four k minus three four k minus three that exactly the same cancel it out. So we just have two leftovers. Two is the answer. So how simple is that? Okay?

Getting the idea guys? So see how we utilize the factorization that we’ve done in the previous part. But see how the numerator there’s a and one there’s nothing common, so we just leave it as a minus one, we can’t simplify any further we can’t factorize but a squared and a what’s common the pronumeral a is common. So I’m going to take a out a squared divided by a is a because or we can think of it this way a times a is a squared so that’s why we have a left inside here and if I take a out, we’ll just have one left. It’s not zero.

Make sure you don’t do that it’s one because a divided by a is one and cross they’re the same. So we just had a leftover which is the answer okay? So cancel cancel. Do some factorizing see how on the top, what’s the common factor guys? x is a common factor and I think it’s the same for the denominator as well. See how 9x and x squared? x is the common factor, isn’t it? So for both top and bottom, we can take out x like this, so the top if I take x out that 3x squared would just become 3x because one of the x goes out and x that becomes one okay?

And here if I take the x out we’ll just have nine and x squared just becomes an x because we take out one of the x and you can see that the co we don’t these are not common but the x and the x, they’re common, so we can cancel it out, so we just have three x plus one over nine minus x left and we can’t go any further.

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