Addition of Algebraic Fractions: Difference of Squares

Addition of Algebraic Fractions Monic Expressions
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24! Let’s do the same kind of thing. I’m going to factorize. And you can see that here, x squared minus 16. 16 is 4 squared, so that’s why I changed it like that. And see here, guys. That, I don’t want negative in front of my x. I kind of swap these around. So it becomes negative 4 x plus 16 and if I factorize that by negative, I’ll get negative 4x minus 16, isn’t it? But see how we have a negative here, so negative negative becomes a positive.

So that’s how I change that to a positive. So it’s positive 3 over 4x minus 16. Get the idea? Always change it like this first! Then it becomes much more simple. So now let’s factorize the denominators. So difference of two squares is x minus 4, x plus 4. And here, the common factor is 4, so just take 4 out. So we just have x minus 4 left, okay? So now let’s compare the denominators. Okay, we’ve got x minus 4 here and we’ve also got x minus 4 here, so the only thing they don’t have here is the x plus 4, and the only thing they don’t have here is the 4. So that’s what I’m gonna do.

So multiply top and bottom by 4 for this fraction and multiply top and bottom by x plus 4 for this fraction. So multiplying by the factor that they don’t have. So now we can see that 2 times 4 is 8, 3 times x plus 4 is 3x plus 12 and you can see now we have the common denominator, now we have the same denominator, so now we can add the numerators. So you can see that 8 plus 12 is 20. The answer is 3x plus 20 over that same denominator. Get the idea, guys? That is the answer. So the key thing, as I said, is making the same denominator, so multiply top and bottom by the factor that each fraction does not have on its denominator.

Okay, let’s see if we can, first of all, take out the common factors. So you can see here, um I’ll put over here, 9x squared is the same thing as 3x, the whole thing squared, and 16 is 4 squared, so it’s difference of 2 squares, so that’s why I did 3x minus 4, 3x plus 4 for those who didn’t realize, okay? That’s what I did there.

Now here, you can see that 7 is a common factor, so take the 7 out and we’ll have 3x minus 4 left, okay? And you can see 3x minus 4 is common for both fractions but this fraction doesn’t have 7 and this fraction doesn’t have a 3x plus 4. So that’s what we’re going to multiply top and bottom by for each of those fractions. Like this because this one doesn’t have 7. We multiply top and bottom by 7 and because this one doesn’t have 3x plus 4.

We multiply top and bottom by 3x plus 4 and simplify like that. And you can see now we have the same denominator. So now we can subtract the numerators. So 7 minus 3x minus 4, minus plus is minus, so make sure you change that, and then you can see that 7 minus 4 is 3. So 3 minus 3x over the same denominator.
That is the answer, okay? I know it looks pretty big because of the denominator but that’s the simplest form, okay? So that’s how we find common denominators. I hope you guys give yourself extra practice after you watch this video.


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