write-each-rational-expression-in-simplest-form-and-list-the-values-of-the-variables-for-which-the-8

Question

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined.
$\frac{8 a b-4 b^{2}}{6 a b}$

Martha Richards · Accepted Answer

Okay, so we&#x27;re going to reduce this rational expression as well as list the values of the variables where this rational expression will be undefined. So we start with the undefined part because we want to do that before we reduce things. And so we look at the denominator and win the denominator when either A or B zero, this will be undefined. Because when we multiply any number by zero here, that&#x27;s going to be zero and zero. And the denominator means on defied. So if a a zero or be a zero than this will, this expression here will be undefined. So now let&#x27;s get to reducing. So whenever we add or subtract in the numerator and we just have only multiplication in the denominator, we just separate this out so we&#x27;ll have eight a. Be divided by 6 80 minus four b squared over six a. B. So here, when I have these a B and a B, those are going to cancel out and you see that we have common factors here. So we have a common factor of two, so I&#x27;ll have divide top and bottom by two. I get four in the numerator and three in the denominator and then also trapped here and again. We have common factor of two. So this will become a two. This will become a three. The A stays as is, and we lose this be. And we only have one left up top here. Right? So it&#x27;s a B squared, which you could also write as b squared minus one, because that&#x27;s the rules of exponents. And so then you&#x27;re left with just a B because two minus one is one in the numerator, so I have to be in the numerator and a three a and the denominator.

Martha Richards · Answer

All right, so we&#x27;re given this rational expression here and were asked to simplify it. But we&#x27;re also asked to provide the values that for the variables that make this undefined so undefined would be when the denominator is zero. So we do this before, really? You know, before we reduce anything or simplify anything because this is the original expression. So when this is the original expression, any time the denominator is zero, we&#x27;re going to get an undefined. So we just set 12 a equal to zero. So for a equal to zero, this would be when it&#x27;s undefined. Now, when we want to simplify, remember when I have addition in the top and division in the bottom, it&#x27;s just each one of these things separately. So I have 12. Ay, ay, ay over 12. A plus 16 over 12 A. So here we see that they share a common factor of four. So if I divide top and bottom by four, then I&#x27;m going to get here All that a two and the 12 I will get a three. And then these ays cancel and again because this eight of the one and eight of the one you can also do subtraction. So a to the one minus one would just be eight of the zero, which is one. So they just cancel out here as well, depending on how you like to think about it. So here I get a 2/3 is what I&#x27;m left with. And then again, we have a common factor of four. So this will become a four, and this is three and the A stays, so we&#x27;ll have four over three a.

Bahar Tehranipoor · Answer

and this question. Want to simplify this expression? We want to find where it&#x27;s undefined. So first, let&#x27;s fact earthy numerator so we can take out a four. Do that. We&#x27;ll get a squared minus four, and we can also factor this into keep that for a minus two times eight plus two. So usually when you see a term squared minus some constant, it&#x27;s really easy to factor it. And then in the denominator, we can also take out of four, four times eight plus two and we&#x27;ll have overhears and thing. Four times it was two. And now let&#x27;s see what we can divide out. We can divide out that four divide out in April&#x27;s too, and very simply, we&#x27;re left with a minus tube. That&#x27;s her answer. But to find words undefined, we have to look at the denominator of our original expression and see where that will be. Zero. Because the denominator zero, the expression is on the fine. We have four day plus eight equals zero, and if we really quickly saw that, we get that A cannot equal negative too, because then we haven&#x27;t undefined equation

Martha Richards · Answer

All right, We&#x27;re given this rational expression here were asked to put it in simplest form, as well as provide the values for B that would cause this rational expression to be undefined. So what we&#x27;re gonna do is take the denominator and said it equal to zero, because when the denominator is zero, that would make this rational expression undefined. And so here I&#x27;ll put the add B square to both sides and I take the square root then and that gives me be. And remember that I have to add that plus and minus here. So I get plus and minus two. So when B is either a positive two or a negative to, this makes the rational expression on defined. And then what we&#x27;re gonna do here is gonna multiply this hour and also factor this denominator. So we&#x27;ll start with the top and numerator. I have three minus and treat. This is a minus one here and distribute this out to both terms. So I get a minus b and then a negative one times. A positive one is a minus one, and so then I can combine the numbers, so this would be a positive three minus a one gives me a negative B plus two in the numerator and then the denominator. This a perfect square. This is a perfect square, and when that happens, I get with no middle term. Here I get to plus B times two minus B and here just rearranging the top. I could rearrange the chop to have the two and front to minus B over two plus B two minus b, and then you can see the fees to terms will cancel and I&#x27;m left with the one in the numerator and a two plus B in the denominator. You can swap these around, and this would become one over B plus two.

Martha Richards · Answer

All right, so we&#x27;re given this rational expression and were asked to reduce it as well. Is this the values of the variables that makes this rational expression undefined? So what we&#x27;re gonna do is look in the denominator 1st 2 less when, What Value seek. I would have to be in order to make this undefined. And that happens when this zero. So if I set this equal to zero and I&#x27;ll just sort of do it off to the side here, plus 16 see you. Actually, it does kind of make it a little bit easier. Thio pull out common factors here first. So I see that in eight is common as well as a C. So if I pull out an eight C that I&#x27;m left with a C plus two and so you notice if you multiply this back out, is that I have 80 times. See, that&#x27;s eight squared plus eight times to a 68 c. Times two is a 16 c. So we get back to where we started. Which needs to happen are for those two things to be equal. So now these are two separate things that if I multiple If this becomes zero or if this becomes zero because it&#x27;s two separate things on multiplying by each other. And when we multiplied by zero, if this side here is zero, the whole thing becomes zero. And if this side over here is there, the whole thing becomes zero. So we&#x27;ll say each one of these separately, equal to zero. So we see here when CIA&#x27;s equals zero were undefined. And then also, if I say C plus two is equal to zero solving this subtracting two from each side, I get sea of negative too. So both see equal to zero or negative two makes this rational expression undefined. And then here we&#x27;re going to now go and reduce this So I&#x27;m still going to use this thing here. So I have this eight c squared in the numerator and then my factored form. Uh, the denominator is 80 times in parentheses, T plus two. So here you can see that this eight and eight work will cancel. And you can only do that because these are multiplied by each other. And then we also have a C square and a C so we can get rid of one of the seas up one of the seas up here with one of the seas down here. It&#x27;s also the same too, right? See two minus one and we get C to the one here. But we just generally notation wives, leave the one off. So I&#x27;m left with a C and the numerator and then a C plus two in the denominator.

Georgiann Andersen · Answer

Okay, so this problem is number two. And they&#x27;re saying that if a over B equals C over D, then is a plus B overby equal to see plus de over tea. Well, if you take a must be over b and expand that out, that it&#x27;s the same missing a plus B plus people speak If you take the c plus d all over D and explain that out, it&#x27;s gonna be C over D l S D over teeth A plus B. If we now be over, B is actually going to be one same way on this side D over D could be simplified toe one. So if we know a over B equals C over D and we&#x27;re gonna add one to each side, we&#x27;re definitely going to still be the same. So your answer is yes.

Problem

Write each rational expression in simplest form a…

Problem 18 Hard Difficulty

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined.
$\frac{8 a b-4 b^{2}}{6 a b}$

Answer

$\frac{4 a-2 b}{3 a}$
$a, b \neq 0$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Heather Z.

Caleb E.

Kristen K.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

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$\frac{4 a-2 b}{3 a}$$a, b \neq 0$

Algebra 2 and Trigonometry

Heather Z.

Caleb E.

Kristen K.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Heather Z.

Caleb E.

Kristen K.

Michael J.

$\frac{4 a-2 b}{3 a}$
$a, b \neq 0$

Ann Xavier Gantert

Algebra 2 and Trigonometry