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Question

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined.
If $\frac{a}{b}=\frac{c}{d},$ then is $\frac{a+b}{b}=\frac{c+d}{d} ?$ Justify your answer.

Georgiann Andersen · Accepted 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.

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

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 have this rational expression here and were asked to simplify it, as well as provide the variable the values for the variables that would make this undefined. So any fraction is gonna be undefined when the denominator is zero. And so here, even though these guys they&#x27;re gonna end up canceling this is the original expression. And so this bottom here can&#x27;t be zero. And so if we just sat 21 be cubed equal to zero, then be is going to be equal to zero. This wind B is equal to zero. This would lead to it being undefined. And then now we&#x27;re just going to reduce. So we see here that the 14 in the 21 are both the visible by seven. So this will become a two, and this will become a three. And then I have four bees up above and three below. You can do the four minus three, cause that&#x27;s the rules for, um exponents. But also I just the way I think about it, as if there&#x27;s three here. We get rid of three here, and I&#x27;m left with just be too the one. So the final expression is two times be over three

James Kiss · Answer

we have a C minus 80 plus P. C minus B D over a C minus 80 minus B c plus B demeaned factor. Both the numerator is now later. So the numerator let&#x27;s group. It&#x27;s four terms. So we group we can take out on a from the first group. But the C minus do you take out a B from the second group but the C minus t for your home and see my honesty and we check out a plus B so si my s t times a plus b denominator four terms route through the 1st 2 together roof the 2nd 2 terms together First group take out a left with C minus t second group could take out, um, a negative be left with C minus. Do you know we have a common c minus D in what we took out a minus bi So C minus T times a minus beat and the C minus diesel cancel, leaving us with a plus B over a nice B in lowest terms

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

Problem

Write each ratio in simplest form. $12 : 8$

Problem 2 Easy Difficulty

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined.
If $\frac{a}{b}=\frac{c}{d},$ then is $\frac{a+b}{b}=\frac{c+d}{d} ?$ Justify your answer.

Answer

Yes

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Catherine R.

Anna Marie V.

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Absolute Value - Example 1

Absolute Value - Example 2

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Algebra 2 and Trigonometry

Catherine R.

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Absolute Value - Example 1

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Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Anna Marie V.

Maria G.

Michael J.

Ann Xavier Gantert

Algebra 2 and Trigonometry