Algebraic Fractions: Simplify by More Denominators

Algebraic Fractions Simplify by Multiple Denominators


Okay, it’s getting a little bit bigger but don’t be afraid. What do you need to do here guys?
See how they already factorize the denominators for you. What I want you to do is put in all the different types of varieties of factors on the denominator. Now you’re probably going what does that mean. Well basically see here.

Both of them have an x minus 2, that’s common, isn’t it? Now the only difference is that this one has an x plus one and this one has an x minus three, so what I want to do is if I multiply this one by x minus 3 and this one so if I multiply this by x minus 3 and this by x plus 1 they would have the same denominator right? So I just multiplied by that what this denominator doesn’t have and I multiply this side by what this denominator doesn’t have okay? So like that, then I would get the same denominator wouldn’t I? But make sure you if I do something to the bottom I must do the same thing on the top just like this. So x plus 1, I have to multiply to both top and bottom, x minus 3, both top and bottom. Don’t get confused here guys the only confusing part is that it’s big okay?

So trying to keep very very close attention. So now we’ll have seven times x plus one which is seven x plus seven times one which is seven and then we have three times x which is three x three times minus three which is minus nine. That’s what goes and are the numerator and then the denominator, it’s this part and this part which is the same, x minus 3 times x minus 2 times x plus 1 like that. It doesn’t really matter which order you put it in so I just put it in any order like that okay? Now simplify the numerator. Don’t worry about expanding or simplifying the denominator that is the simplest form, so don’t go any further with the denominator leave it as it is, and then 7x plus 3x is 10x 7 minus 9 is minus 2. That’s the answer.

Don’t go any further! That’s the simplest form okay? See how both fractions, they have x minus 4 commons but this fraction, this denominator has an x but it doesn’t have an x plus 6, so I’m going to multiply it by x plus 6 for this denominator and this denominator, it has x plus 6 but it doesn’t have an x. So I’m going to multiply by x but you know that I can’t just do that I have to do the same thing on the numerators don’t I?

So I’m going to multiply this fraction by x plus 6 on both top and bottom and this fraction by x on both top and bottom, so whatever each of each other doesn’t have you multiply by it. So now 1 times x is x, 1 times 6 is 6, and then 1 times negative x is negative x, always follow the signs in front and then the denominator is x times x plus 6 times x minus 4, or you can put it like this whatever order doesn’t really matter. So now x minus x. What’s that? They cancel, don’t they? That’s zero. So we just have six over that big denominator. I just don’t want to repeat it again and again okay?


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