Then in the denominator, we can factor a squared minus let me do that in a different color. If you ever want to say, hey, why does this work? Just multiply it out and you'll see that when you multiply these two things, you get that thing right there. Then in the denominator, we also have an a plus 2. We've multiplied it, we've factored out the numerator, we factored out the denominator.
Let's rearrange it a little bit.
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So this numerator, let's put the a plus 2's first in both the numerator and the denominator. So this, we could get a plus 2 in the numerator, and then in the denominator, we also have an a plus 2. In the numerator, we took care of our a plus 2's. That's the only one that's common, so in the numerator, we also have an a minus 2. Actually, we have an a plus let's write that there, too. We have an a plus 1 in the numerator. We also have an a plus 1 in denominator.
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In the numerator, we have an a minus 2, and in the denominator, we have an a minus 1. So all I did is I rearranged the numerator and the denominator, so if there was something that was of a similar-- if the same expression was in both, I just wrote them on top of each other, essentially. Now, before we simplify, this is a good time to think about the domain or think about the a values that aren't in the domain, the a values that would invalidate or make this expression undefined.
Like we've seen before, the a values that would do that are the ones that would make the denominator equal 0. So the a values that would make that equal to 0 is a is equal to negative 2.
You could solve for i. You could say a plus 2 is equal to 0, or a is equal to negative 2. Subtract 1 from both sides. Or a minus 1 is equal to 0. Add one to both sides, and you get a is equal to 1. For this expression right here, you have to add the constraint that a cannot equal negative 2, negative 1, or 1, that a can be any real number except for these. We're essentially stating our domain.
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We're stating the domain is all possible a's except for these things right here, so we'd have to add that little caveat right there. Now that we've done that, we can factor it.
We have an a plus 2 over an a plus 2. We know that a is not going to be equal to negative 2, so that's always going to be defined.
When you divide something by itself, that is going to just be 1. As you can see, there are so many things going on in this problem. Start by factoring each term completely. The problem will become easier as you go along. Note that the x in the denominator is not by itself.
How Do You Multiply a Rational Expression by a Polynomial?
This is a common error of many students. I am sure that by now, you are getting better on how to factor. Multiplying Rational Expressions Rational expressions are multiplied in the same way as you would with regular fractions. Download Version 1.
Is multiplication of rational expressions commutative? | Socratic
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