Fractions involving Quadratic Terms: Common Factors
Transcript
See! 2 is common and same here, 3 is common, so take out your common factors first.
So take 2 out and here take 3 out and make sure you got the right remainders in the brackets, okay? So now that we’ve simplified that by taking our common factors. Now we can apply our quadratics. So on the numerator, I’m going to use my x and x and because it’s negative 2. I’m going to use positive and negative. So I’m going to start with positive 1, okay? And see if I can get it all work out. So x times positive 1 is positive x and the other one will probably be negative 2, isn’t it? Because 1 times negative 2 is negative 2. And then across them, find the product.
So it’s going to be negative 2x. And let’s check! x minus 2 is negative x that’s what we want. And as I said guys if you do happen to not get the right combination or the right pair at the beginning. Don’t worry. Try the other pair or maybe switch around the signs or something, okay? So don’t be worried if you don’t get the right ones at the first go, okay? So anyway we’ve got that. So it’s going to be x plus 1 and x minus 2. And that’s what I put there on the numerator and you can see that 4 is 2 squared.
So again we have a difference of two squared. So the denominator will be x plus 2, x minus 2, isn’t it? So let’s see we can cancel these out. They’re common, so we’ve just got this part left which is the solution, okay? Let’s do this! Starting with okay what I’m going to do is start with the top, x and x and then I’ll work on the denominator.
Well, first of all, the top, it’s positive 5, so it could be positive positive or negative negative but that’s negative. So we need to use negative negative. So it’s going to be negative 1 which makes negative x and negative 5 which makes negative 5x and clearly negative x minus 5x is negative 6x which is exactly what we want.
So I’ve got the numerator. Now for the denominator, well first of all I just put the numerator factorizations in. x minus 1 and x minus 5. Now for the denominator, you can see that 2 is a common factor, so again make sure you take out the common factor first, like that. And then, now we’ll look at the factorizations of the brackets. So x and x, you can see that it’s positive. So it’s positive positive or negative negative but that’s negative, so negative negative is what we want. So I’m going to use negative 3, so the other one will be negative 5 because that’s 15.
So negative 3x and the other one be negative 5. Cross them! Multiply! And then you can see that negative 3x minus 5x is negative 8x which is that, okay? So factorize them correctly, please check if you’ve got that. Now put in x minus 3 and x minus 5 inside this bracket just like that. And you can see that these are common, so cross them out. And we’ve just got that left okay.
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