in-3-20-perform-the-indicated-additions-or-subtractions-and-write-the-result-in-simplest-form-in-e-5

Question

In $3-20$ , perform the indicated additions or subtractions and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined.
$$
\frac{y+2}{2}+\frac{2 y-3}{3}
$$

Derrick Hanson · Accepted Answer

we&#x27;re being asked to add these two fractions, but we have a problem because in order to add or subtract fractions, we have to have a common denominator. And these do not is the first thing that we would need to do is try and find some number that both two and three can multiply up, too, so they&#x27;re denominators would be in common. In this case, I would say the least common down to the lowest number of the two and three can both multiply up to would be six. So our goal right now is we want to rewrite both of these fractions so that they are over six. Then once we&#x27;ve done that, we can actually combine them together. All right, so let&#x27;s start with why. Plus 2/2. If I want to get y plus 2/2 to be something over six, I would definitely need to take two times three. But if I&#x27;m going to take that denominator Times three, I would also need to multiply that numerator by the exact same thing, which means I&#x27;m going to take the quantity of Y plus two times three is well, that means we need to distribute that three, right? I know that&#x27;s not written the way you&#x27;re used to seeing it. Normally, you guys, we&#x27;re used to seeing it written like this, but we would still want to. This is still a distributive problem, and so we still want to be using that property. So we&#x27;d be taking three times. Why gives us three why? And three times to gives us six. So we would have three y plus 6/6. So there&#x27;s one fraction. Now I need to get the second fraction. That is to why minus 3/3. We also need to change that to something over six. Well, to get from 3 to 6, we would need to multiply by two. But if I&#x27;m gonna multiply the denominator by two that I would have to multiply the numerator by the exact same thing. This is a quantity of two y minus three. So that would mean we have a distributive property again. Two times two. Why would be four? Why, two times negative three would be negative. Six. Now that we have a common denominator, I can actually combine these. Remember, when we add or subtract fractions, we do not combine the denominators, we just rewrite it. Meaning it is still going to be over six for the numerator. We want to combine like terms. So I have a three y and a four y three y plus for why would be seven? Why? I have a six and I have a negative 66 plus negative six would be zero. Meaning we don&#x27;t really need to write that. We just have seven. Why over six? There isn&#x27;t anything that 76 have in common that I am aware of, which means we aren&#x27;t able to reduce this fraction, so that would be an answer.

Georgiann Andersen · Answer

we&#x27;re gonna simplify the following expression says number chat our Expressionists a plus one all over three A. We&#x27;re gonna add rehouse to this. In order to do this, we have to have the denominators the same. So we&#x27;re gonna take two times if it&#x27;s one all over two times three A. Remember what you did to the bottom. You have to do the top. And then the next one, we&#x27;re gonna take the three times the three a and the two times the three that&#x27;s gonna leave us with two es plus two all over six A was nine a over six A. So we&#x27;re gonna have to a plus two. That&#x27;s nine a all over six A that&#x27;s gonna leave us. We&#x27;re gonna combine their like terms. That&#x27;s gonna be 11 a plus two all over six a. And that is our are this week. And simplify that, too. Um, the factors that would make this undefined would end up being zero, so they cannot be zero

Alisa Lu · Answer

So this question were asked to do this attraction and then also list any values for the variable X, which the fractions are not defined. So right off the bat, we can say that wife cannot be equal to zero, as that would make the denominator here equal to zero. And we can&#x27;t have that. So to do the subtraction, we need Thio find a common denominator. So in this case, the common denominator would be too I So I would have to multiply five by two. I over to I, which gives me 10. Why? Over to y minus one of the two I. And so then this would combine into 10. Why minus one over to I, um c could, I guess, simplify this a little bit more after splitting the fraction. But that would just give you get you back to where we started. So we can just leave her answer like this. 10 Y minus one over to us.

Derrick Hanson · Answer

we&#x27;re being asked to add these two fractions together to see what we can get for an answer Any time you are adding or subtracting fractions, the number one thing that you have to make sure you have is a common denominator. You cannot add or subtract fractions without a common denominator. In this Problems case, that&#x27;s not really a problem for us, because each of these fractions has a denominator of three. So we don&#x27;t have to do any work to do that. We already have a common denominator. We&#x27;re ready to go ahead and combine. All right. So any time you&#x27;re adding or subtracting fractions, once you have a common denominator, remember, you do not combine the denominators you simply rewrite. Meaning we have a common denominator of three. So our answer is also gonna be having a denominator of three. You Onley combine the numerator, the tops of the fractions. So when I&#x27;m actually doing here is X plus two x Okay, well X plus two X, or you can think of it as a one X because remember, there&#x27;s always an invisible one in front of that in front of any variable. If we don&#x27;t show a coefficient. One plus two is three. So we would have three ex over three. We did combine them. But after you&#x27;ve combined with adding or subtracting fractions, you should always check to see if possibly you can simplify further. In this case, we certainly can, cause we can see we have a three in the numerator and a three and the denominator. So we are able to go ahead and cancel those out, leaving us with a final answer of simply X.

Derrick Hanson · Answer

first thing I noticed with this problem is that one term is written as a fraction and one term is not. I do not like trying to solve that math problems where I have different pieces being expressed in different forms. Just I think it just opens you up to accidentally making mistakes that you&#x27;re better than so first thing I want to do is rewrite this and so that a can be represented as a fraction. I&#x27;m simply just going to put it over one. Right? A over one is certainly the same thing as a cause. Anything divided by one is itself. So that&#x27;s that&#x27;s fair. So I&#x27;m really doing a over one minus 3/2 A. All right now, I can see I do not have a common denominator here, so I&#x27;m gonna have to find one. Since one can be multiplied by anything, I&#x27;m not gonna need to multiply both fractions by something. I can already tell that I&#x27;m going to be able to just rewrite my second fraction because I should easily be able to get my fraction of a over one to change into a fraction that has to a for its denominator because I know that if I take one times to A, I will get to a now the catches just like with everything else we&#x27;ve been doing. If you want to change a rewrite a fraction and not change its value, whatever you multiply the denominator by you also have to multiply the numerator by meaning we have to take a times to a well a times to a would be to a squared right. Eight times a is a squared to is along for the ride Essentially. So my first fraction instead of a minus one could be expressed as to a squared over two A. I now have a common denominator, which means I am ready to combine these. Remember, when we combine fractions by adding or subtracting, we do not combine the denominators. We just rewrite it. That minus has nothing to do with the denominator, right. If you have a negative fraction, remember for a negative fraction, you can choose whether that negative is attributed to the numerator or the denominator. We don&#x27;t want to put that negative to the denominator because then they wouldn&#x27;t be in common, so instead just attributed to the numerator and will take to a squared minus three. Well, to a squared minus three would give me to a squared minus three right to a squared and three or not common terms. Not like terms. So I can&#x27;t actually combine those. This just has to stay as a quantity. So this would be my answer. You can&#x27;t reduce anything because everything in the numerator is together as a quantity. So unless you have exactly to a squared times three, then to a start here. So unless you have exactly to a squared minus three in the denominator, you would not be able to cancel it out. Okay, Now the last part of this, we do have to account for any undefined values for a So I looked back in my original problem. This a is a numerator, as we showed right here, so I don&#x27;t need to worry about that. But I do have a denominator of to a So the question is, if I have to a what value of a would go would cause this equation to be zero, because that&#x27;s what we don&#x27;t want. Well, to time, zero would be zero. So the only problem for this equation would be if a happens to equal zero that would cause our answer to be undefined, which is basically just math word for an air. Right? So our answers to a squared minus three over to a as long as a does not equal zero.

Derrick Hanson · Answer

with this one. I think the first and most important thing is to recognize that one of my terms is expressed is a fraction, and one of them is not one of the easiest ways to accidentally and make a mistake with math problems that we know we&#x27;re capable of doing is to allow a problem to continue to stay where things were being expressed in different forms, meaning, If I see one terms expresses a fraction, I want my entire equation to be expressed as a fraction. It&#x27;s not necessarily required, but I do think it helps if you will be able to visualize better. And it&#x27;s a takes very little time. How do we write? Three is a fraction. Well, any whole number that&#x27;s not written as a fraction just means need to put it over one. That&#x27;s all it means. So I&#x27;m simply going to rewrite this as 3/1 plus two over X. I recognize we could have easily just kept the memory in our head. That three is really being looked at as 3/1. But why not take the time to go ahead and write that just to not make us have to remember more things than necessary. Writing it this way makes it very obvious to me that we do not have a common denominator. So of course we can&#x27;t solve out this problem yet until we have successfully got a common denominator. Well, between one and X, I don&#x27;t think X is going to be able to multiply upto one. That doesn&#x27;t really make sense. But I do think I could multiply one upto X so I don&#x27;t have to mess with my second fraction. Aiken, just rewrite that one to over extend, stay two of Rex. But 3/1 needs to be changed. I need to change this into something over X. Remember, the way that works is whatever I multiply my denominator by, I have to multiply my denominator by as well so that I don&#x27;t change the actual value of the term. Okay, well, we know one times X gives us X or an s pretty straightforward. One times, anything is just itself. So if I&#x27;m going to multiply by X and my denominator, though I also have to multiply by X in my numerator three times X would give us three x meaning. Now we have a common denominator that I know. I can express 3/1 as three x over X. So now that we have a common denominator, we can go ahead and add the&#x27;s. We can combine them. Remember, when we combine fractions, you do not combine denominators. You simply just rewrite it. You Onley, combine the numerator the tops three X plus two. Now I can&#x27;t actually combine those together because they&#x27;re not like terms. So the best I can do is say OK, I have three X Plus two as a quantity. That&#x27;s the best I can do because Three X Plus two is a quantity unless I have exactly the same thing in my denominator of three x plus two, I can&#x27;t cancel anything, so this would be the answer to this problem. However, we do also need to account for any values that might cause this fraction to become undefined. Meaning. Is there any value for X that would cause us to have zero in the denominator? Well, at any point during the problem, the only thing I ever had was an X in the denominator. So if it&#x27;s just X, what would you plug in to make X equals zero. Well, that would be zero. So this problem is great. The answer is three X plus two over X. As long as X does not happen to be zero. Because if x happened to be zero, that would cause this problem to be undefined.

Problem

In $3-20$ , perform the indicated additions or su…

Problem 7 Easy Difficulty

In $3-20$ , perform the indicated additions or subtractions and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined.
$$
\frac{y+2}{2}+\frac{2 y-3}{3}
$$

Answer

$\frac{7 y}{6}$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

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Absolute Value - Example 1

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$\frac{7 y}{6}$

Algebra 2 and Trigonometry

Heather Z.

Alayna H.

Maria G.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Heather Z.

Alayna H.

Maria G.

Kristen K.

Ann Xavier Gantert

Algebra 2 and Trigonometry