write-each-rational-expression-in-simplest-form-and-list-the-values-of-the-variables-for-which-th-17

Question

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined.
$\frac{a^{3}-a^{2}-a+1}{a^{2}-2 a+1}$

Bahar Tehranipoor · Accepted Answer

in this question were given this expression A cube minus a squared, minus a plus one. So what we&#x27;re gonna do in this question? Oh, her the nor mater over my bad. A squared minus to a plus one. There you go. So we want to simplify this, and we want to find the values of pay where this function is not true. And that would be where the denominator equal zero. Well, first, let&#x27;s simplify this. So I think the denominator just looks easier to simplify. So we&#x27;re gonna start with that. What we can do is we could just factor that and it will be a minus one squared, and we can actually check that. If we multiply that through, we will get a square minus two equals one. Now, in the numerator, this looks a bit harder to factor. But there&#x27;s actually really cool triggered. I&#x27;m gonna show you. So you have this a cube term in this negative a term or right over here. Then we have this negative a square term in a positive ones. We have negative a squared plus one. Now we can a fact or something in the a cubed minus a so that we get a squared plus one or negative a scrip us one. If we factor out a negative, eh? We will get negative a squared plus one. And if we just factor a one here, of course, it&#x27;s just gonna be negative. A scripless one. Now, if you add these factors and multiply it by negative a script is one. That is how you factor this expression. So it&#x27;ll just be negative. A simple, sworn soldiers, right as one minus squared times one mine is a and that&#x27;s it. And actually, I think it&#x27;s easier if we just take out the like a negative here. So instead of writing one, mine&#x27;s a score times one minus a week in just right a minus one was putting negative right there and then one minus a squared. So now what can we cancel out? Weaken? You can see we can Kids allowed that a minus one thing. Kids love that factor right there, and we can multiply this negative end So we have we can write as a squared minus one instead of this woman is a square times of negative. So your face reminds one over a minus one and I&#x27;ll Google any page or quick, so it&#x27;s easier to see that. So right now we have a squared minus one over a minus one. We can factor that ice cream ice one again. So we get a minus one times eight plus one over a minus one. Divide these out and you get a close one. So that is your simplified expression. But we have to go back real quick and look at our denominator and say What are the values of a where this doesn&#x27;t work? So of course, if we plugged in a equals one, we would get zero The denominator in this expression, we&#x27;re not work. So even though we can end up simplifying into April&#x27;s won, there is still the value of a equals ones. We say they cannot equal one where this expression would give you zero in the denominator

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.

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

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 asked to simplify this rational expression and also list the values of the variables for which this rational expression would be undefined. So the first thing I would do is find the undefined part, because once these things cancel, you can see these. They&#x27;re gonna cancel here. Then this will no longer have a denominator that cannot be zero. So what we have is is that we can&#x27;t have zero down here. So if 10 a is equal to zero than it is undefined and so then that means just the A equal zero is when this is this rational expression is undefined. And then now we can just redo. So when I have a five and the numerator and attending the denominator both these air divisible by five So this becomes one. And this becomes too. When you have two A&#x27;s above and one below, you can get rid of one and you keep just one, eh? So I&#x27;m left with in the numerator a be over too

Leina Wu · Answer

Okay, This question. We are simplifying a complex, rational expressions the one plus three over B plus two over the square divide by one liners, one over b squared. In order for us to simplify this expression, we need to take care of these denominator B B Square and A B squared. So we need to multiply everything by a common denominator common dominator, apparently by B and B Square. We can tell the common the least. A common denominator would be be square. So let&#x27;s multiply everything by three squares when one plus three would be plus two over the square times the square on the bottom. We have one Mina&#x27;s one over B squared times speaker, but let&#x27;s distribute the B square to all the terms inside of the open pregnancies. So the first multiplication we&#x27;ve got us be square 2nd 3 Overbey times be square that IHS the Read Be and then to over the score times be square the beast. Where would be reduced? We get to but the bottom one time speed square. We have B squared now one of the B squared times be square and that&#x27;s one. Keep going. We can factor the top. The new murder could be factored as B plus two times B plus one. In terms of the denominator, confected eyes will be plus one times B minus one. So if the requirements of match we can, we can divide both the top and bottom by B plus one. We get B plus two over B minus one. So this is the simplified form. The simplified form can be done. Okay, when the requirement of this rational expression are satisfied. Which means if you see a denominator, 11 is one of would be squared is cannot do zero. There are, like other denominator, as be square cannot be zero and b cannot be zero. Well, let&#x27;s see, in the 1st 1 we have won over Bay Square cannot be won, which means B squared cannot be one of the one. So being squared cannot be won. You cannot be plus or minus what we&#x27;re just a square root of what the second and third requirement tell us. Being cannot be zero. So in journal, if you look at the beast, our beat cannot be zero cannot e plus minus one. And then the simplified form of this expression will be B plus two over B minus one

Problem

Write each rational expression in simplest form a…

Problem 27 Hard Difficulty

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined.
$\frac{a^{3}-a^{2}-a+1}{a^{2}-2 a+1}$

Answer

$a+1$
$a \neq 1$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Grace H.

Alayna H.

Caleb E.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

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$a+1$$a \neq 1$

Algebra 2 and Trigonometry

Grace H.

Alayna H.

Caleb E.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Alayna H.

Caleb E.

Maria G.

$a+1$
$a \neq 1$

Ann Xavier Gantert

Algebra 2 and Trigonometry