in-3-20-perform-the-indicated-additions-or-subtractions-and-write-the-result-in-simplest-form-in-e-4

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.
$$
\frac{a-1}{5}-\frac{a+1}{4}
$$

Alisa Lu · Accepted Answer

Okay, so this question were asked to perform subtraction on these two fractions, we have a minus one over five bias, a plus one over four. So these two don&#x27;t have any hate limiting factors for a as a Zen, the numerator and can equal anything, and you&#x27;re real number. But what we do need to do is make the denominators a common denominator. And to do this, the greatest common factor for the least common multiple for these two would be 20. So for the first fraction to equal have a denominator 20 money to multiply by four before this gives us for a minus for over 20 and for the second fraction, to be equal to have a denominator of 20 minutes need to multiply by five over five, which gives us five a plus five. Okay, so now we can just go ahead and do more. Most attraction, I guess, on the numerator. So here will have for a minus 5,000,000 which gets you negative A and the negative four minus phi, which gives your negative not so final answer is negative. A minus nine over 20

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 for this question, were asked to combine these fractions and then also define any values of the variable X, which the fraction is not defined. So right off the bat and consider ex cannot equal to zero because that would make this denominator zero, and we can&#x27;t have that. So you combine these fractions, we need to find a common denominator. So one can be re written as one over one and still get a common denominator. We just need to multiply one by X over X to spend becomes one over X plus X over fix, which then becomes one plus X over X and you can&#x27;t reduce this anymore. So that&#x27;s your final answer.

Georgiann Andersen · Answer

bringing its simplify the following expression. This is question, eh? Our expression is a plus five all over five A subtracting a minus eight allover. Hey, In order to start this, we need to have the same denominator. So we&#x27;re going to multiply the first fraction my eight, and then we&#x27;re going to multiply the 2nd 1 by five. Remember what you do to the top. You have to do the bottom that&#x27;s gonna turn out to be a plus. 40 all over. Were you a? And the next one is gonna be five a minus 40. Well, over 40 eh? So we&#x27;re gonna have a plus 40 minus five a minus, a negative 40. Which is Seamus adding 40 all over. Fourty, eh? Now we&#x27;re gonna combine the like terms, so we&#x27;re gonna have three a 80 all over 40 eh? And that&#x27;s our answer. We can&#x27;t take that any farther. But he also said to identify what, um, would make this undefined to make it undefined. A cannot equal to 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

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.

Problem

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

Problem 6 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.
$$
\frac{a-1}{5}-\frac{a+1}{4}
$$

Answer

$\frac{-a-9}{20}$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

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Catherine R.

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Kristen K.

Absolute Value - Example 1

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$\frac{-a-9}{20}$

Algebra 2 and Trigonometry

Grace H.

Catherine R.

Alayna H.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Catherine R.

Alayna H.

Kristen K.

Ann Xavier Gantert

Algebra 2 and Trigonometry