Algebraic Fractions: Simplify by Denominators

Algebraic Fractions Simplify by Denominators


Okay, this time we’re adding but this time look at the denominators. We need to make common denominators in order to merge them together right?

But the denominators, they’ve got some pronumerals involved. So what do we do? Remember guys what I said before in one of the earlier questions I said if you like you can just multiply with each other, so I’m going to multiply this fraction by a which is this one here, so make sure you do it to both top and bottom.

And then with this fraction, I’m going to multiply by a minus 6 on top and bottom okay? So when I do that I’ll get 2 times a which is 2a and then we do a minus 6 times 2 right? So this part here guys, if you like you can add in some extra steps I just did it in one go but have a look! This underline part here it’s 2 times a minus 6 isn’t it, so it’s basically 2 times a minus 6 like that, so 2 times a is 2a and 2 times negative 6 is negative 12. That’s how I got that numerator, so add an extra step if you need to always add extra steps okay? If you need to always do that.

And then the denominator sees how a times a minus 6 is a a minus six and same here a times a minus six times a is a a minus six, so we have the same denominator.
That’s why we keep that as the denominator. So now two a plus two a is four a minus 12 over the same denominator, that’s the answer. We can’t go any further that’s the final answer, all right?

So again!!!
We’ve got some pronumerals on the denominators so we have to make the same denominator by multiplying by each other. So for this fraction, I’m going to multiply m plus 3 and for this fraction, I’m going to multiply by m plus 1 like this but make sure you go to both top and bottom. So this fraction by m plus 3 on top and bottom and this fraction by m plus 1 on top and bottom. And then again I’m going to expand it, so the denominator now becomes m plus 1 times m plus 3 right? And then here 4 times m is 4 m, 4 times 3 is 12. 2 times m is 2m but we have the negative there, so the negative goes out front and negative 1 times 2 is negative 2.

Don’t forget to put the negative there it’s not positive it’s negative okay? So be careful with the signs again if you need guys add in extra steps. So now let’s gather the like terms. 4m minus 2m is 2m, 12 minus 2 is 10. So that’s the answer over the same denominator m plus 1, m minus 3 and plus 3. sorry okay?

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