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So if I want to find out what the implied domain is of this problem, we have two extra rules.
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Remember, our domain is always going to be all our all-real numbers except for when we are divided by zero,
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cannot be a part of our domain, or when we're taking the square root of the negative number.
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So what I'm going to say is, I'm going to look at all my x values work except for,
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I cannot have a zero on the bottom, so I'm going to say zero.
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I want to figure out what values make giving zero on the bottom.
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So I set the bottom, you always take the bottom of your rational expression and set that equal to zero.
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And then this has to be greater than zero, right?
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You just, this cannot be negative.
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So since it has to be greater than zero, all I'm going to do is I'm going to say five plus x has to be greater than or equal to zero.
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Makes sense.
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These are two equations when you're trying to find your domain that you want to use.
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I have any questions on this.
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No? Good?
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This has to be greater than zero. This cannot be zero.
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Right? You can't have zero on the bottom, and you can't have a negative number under the radical.
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So now, let's just solve for x.
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So when x is negative three on the bottom, that gives us zero, right?
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And when x is greater than or equal to negative five, that gives us a negative number.
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Right?
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So our domain, so this is a part of your domain.
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You can say that x does not cannot equal negative three, but negative three leads to generally this greater than negative five, right?
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So I really don't need to write x canonical negative three.
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I can really just say all numbers that are greater than or equal to negative five would be your domain.
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But since you're just getting used to you guys knowing x, x, canonical negative three is involved in this, but all this red stuff leads to you guys can remember.
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There's only two ways that you're not going to include in your domain.
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When it's zero on the bottom, or when it's negative.
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So to do that, you set your bottom equal to zero, and you set your root equal to greater than or equal to zero.
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And then solve for x, and that's what it is.
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So you can say your domain is, well, it's not for this one here.
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You can use all real numbers, but it's not really, it's only all real numbers that are greater than or equal to negative five.
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So it's really not all real numbers.
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We like to use all real numbers when there's maybe not a root on top, because it is all the numbers except for one number, which would have been a negative three.
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But when you have a constraint with the root, it's only all numbers that are greater than negative five.
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So we don't want to write all real numbers except for those, because that's clearly the line of numbers.
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Any last questions on that?
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No? Good?
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Can you do a number six?
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Sure. So...