in-25-30-perform-the-indicated-operations-and-write-the-result-in-simplest-form-in-each-case-list--4

Question

In $25-30,$ perform the indicated operations and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined.
$$
\left(x^{2}-2 x+1\right) \div \frac{x-1}{3} \cdot \frac{x+4}{3 x}
$$

Alisa Lu · Accepted Answer

So for this question, were given a polling a mule divided by a fraction times fraction. So I&#x27;m just gonna look at the pollen well divided by a fraction. First of so, the polynomial were given its X squared minus two X close one, and this is being divided by X minus one over three. Dividing by fraction is the same as multiplying by. It&#x27;s reciprocal. You can say that. X squared minus two X close. One is being multiplied by three over X minus one. So the numerator over here will factor out into X minus one times X minus one over one times three X minus one. So over here, it&#x27;s important to note that our ex cannot equal positive one, as that would make our denominator here equal to zero. So these X minus ones cancel out and we&#x27;re just left with three times X minus one over one. And now we have to multiply this by X plus four over three X. So now we have to say that our ex can also not be equal to zero, as that would make this denominator equal to zero. So the three here cancels out with this three and now we&#x27;re just left with X minus one times X plus four over X and so that is our final.

Alisa Lu · Answer

So for this question, when given like a string of different operations that we need to perform. So I&#x27;m going to look at the first half right now, which is three x over X minus one times X squared, minus one over X. So let&#x27;s go ahead and constrain our X value. So ex cannot be cool one or zero as thieves would make the denominator equal to zero. So before I multiply across and go to factor out the numerator here and this gives me three x over X minus one times X minus, one times x plus one over X and then I&#x27;m going to do some cancellation. This X minus one cancels with this X minus one and this X cancels with this ex leaving us with just three x plus one under one. Now we need to divide this by X plus one over three. Dividing by X plus one over three is the same as multiplying by the reciprocal of X plus one over three. So we can say that three X plus three times X plus one is being multiplied by three over X plus one. And so here we have to say that our ex cannot equal negative one as that would make our solution. Uh, I mean, our denominators here. So these X plus ones cancel out and we&#x27;re just slept with three times three over one, which is equal to nine. So that&#x27;s your final answer.

Alisa Lu · Answer

So for this question, were given a series of fractions were asked to perform a series of operations on them. I&#x27;m just going to look at the 1st 2 so I&#x27;m going to factor out the numerator here. To be X minus two or times X minus. Waas over for X is being multiplied by a 12 x square and factory out of X here. That will give us X minus two. So from here, we can say that our X value cannot be equal to zero or two, as that would make these denominators equal to zero. So now we can cancel her before here before here, making this three in this actual cancel with one of these X is making this three X. Now, we can say that this X will cancel with this ex just getting rid of the ex entirely. This X minus to cancel this X minus two. And now we&#x27;re left with three times X minus one over one. So this will give us an answer of three times X minus one over one. Now it&#x27;s asking us to the by this answer by X minus one over X, which is the same as multiplying by. There was cyclical of X minus one over X. So you could say that this is equal to three X minus one over one times X over X minus one. So here, in this fraction, ex cannot be zero, and we&#x27;ve already put a limit. Their butt X can also not be equal to one as that, with this denominator equal to zero. So we have to write. X cannot be even one as well. So now we can say that this X minus one cancels with this X minus one. And so we&#x27;re just left with three acts over one, which is just three X s O. That is our answer.

Alisa Lu · Answer

So for this question, they&#x27;re asking us to subtract. Um What? Well, they&#x27;re asking us to do subtraction on this fraction to x squared, plus one over five X minus seven X square minus one over by Lex. And so we have to say that ex cannot be equal to zero, as that would make the denominator evil to zero. So now, from here, we can just go ahead and some tracked because you already have a common denominator to x squared minus seven x Where gives you negative five x squared and then one minus and negative one is same s one plus one. So that&#x27;s just too. And all of this is over five mics.

Georgiann Andersen · Answer

Okay, We&#x27;re gonna simplify. Simplify the following expression. This is number 20. The expression is one over X plus one over X minus two. Subtract two over X squared minus two X. Okay, First thing we&#x27;re gonna do is simplify the third term. You&#x27;re gonna simplify the third turn. So two over x x squared me this two X, it&#x27;s gonna be too over X times X minus two. Then we&#x27;re gonna combine second term with the third term. So we&#x27;re gonna take one over X minus two and we&#x27;re gonna subtract two x times X minus two. Which is gonna be We need to take X times about the numerator and denominator. The first fractions. So it&#x27;s gonna be a over X minus two. Tracked the two over X X minus two and we&#x27;re gonna end up with X minus two O R X times X minus two. We can cancel the X minus twos out, leaving us with one over X. Now we can come fine. The first term with this one. So one over. EPS, it&#x27;s one over X. It&#x27;s gonna be too over x to make this an undefined statement. Ex cannot be zero or two

Derrick Hanson · Answer

we&#x27;re being asked to add these two fractions together, whether we&#x27;re adding or subtracting. The one thing we have to have first is a common denominator, which we do not have here. So our first step is gonna be in try and get these to a common denominator. One denominator is X plus two. The other denominator is X X plus two is a quantity. Unfortunately, it&#x27;s X plus two, not x times two. If we had just had two x and X, this would be pretty easy. We could just multiply the second fraction. By two, we&#x27;d have denominators of two X on both them, and we could add and be done. But that&#x27;s not the case. This is X Plus two. So there isn&#x27;t any way that I can simply get the second fraction too easily equal the same denominator as the first. You can&#x27;t add to top him to the numerator and denominator. That&#x27;s not a thing, right? You have to multiply by something. So unfortunately, there&#x27;s really nothing in common here. Yes, they both have an X, but in one of them the X is bound with the two, and then the other one is just a standalone X. So they don&#x27;t really have anything in common when you have fractions and they&#x27;re denominators have absolutely nothing in common. The only way that you can really go about trying to solve it out is you multiply each fraction by the others denominator. Meaning? I&#x27;m going to take this first fraction of three over X plus two and I&#x27;m gonna multiply it by my second fractions denominator. Namely this X right here. So if I multiply by X and the job dinner, I have to multiply the numerator by X as well. Okay, three times X is three X. I&#x27;m not actually going to multiply out this denominator yet because it&#x27;s possible I may be able to simplify stuff later on. I&#x27;m just going to write it as literally x times the quantity of X plus two. You don&#x27;t have to do that, but remember, we&#x27;ve talked about with the multiplying and dividing rational functions in the section before this. If you can simplify rational expressions, what you have to do is factor the numerator factor the denominator and see if things canceled. So I might as well leave my denominator factored until I know that I can go ahead and multiply back together. Okay, so I&#x27;ve got that for my first fraction three x over x times the quantity of explosives to again. If you don&#x27;t like that, just go ahead and distribute the X. And there it would give you X squared plus two X. You can totally have that if you want. For my second fraction, I&#x27;ve got X minus two over X, and I am going to multiply that by the other fractions denominator, which in this case would mean my first fractions denominator of X plus two. So that&#x27;s what we&#x27;re gonna multiply by on both top and bottom numerator and denominator in my numerator, that means I&#x27;m taking the quantity of X minus two times the quantity of X plus two. So that&#x27;s going to be foiling. Right? First term times, first term X times X is X squared outside terms negative too. Times are how do we first outer Inter, lest so outside terms would be the X and the two doesn&#x27;t really matter. But I&#x27;m gonna try and do it by full just cause I imagine that&#x27;s how most you have learned it. So I figure it&#x27;ll help so X Times two would be two x inner two terms would be negative two times x, so that would be negative. Two X and then last two terms would be negative. Two times two. So negative four in my denominator, just like last time. Instead of actually distributing that X, I&#x27;m simply going to write it as X times the quantity of X plus two. Now, when I write that up here, I&#x27;m going to go ahead and clean up the middle here because two X minus two X would cancel. Right. So I&#x27;m gonna rewrite it up here as X squared minus four over X times the quantity of X plus two because we can see two x minus two X would cancel out. All right, you can see that we have now got ourselves a common denominator. So since we&#x27;ve got ourselves our common denominator, let&#x27;s go ahead and combine. Remember, when we add fractions, we do not combine the denominator. We just rewrite that exactly as it was. We only combine the numerator that we can only combined with like terms, and I don&#x27;t see any here. Remember, an X squared is not alike with Justin X so I can combine these into one fraction. But I can&#x27;t actually combine them together, meaning it&#x27;s just X squared plus three X minus four. That&#x27;s our answer. You could factor the numerator. And if you factor the numerator, what you will see is that nothing cancels. So since nothing cancels, that is our answer, we do still need to determine any values that would give us an undefined problem. So let&#x27;s look back at the original problem. I have a denominator of X plus two in a denominator of X. Remember, what gives us undefined is having a zero in the denominator. So since we can&#x27;t have a zero in the denominator, I&#x27;m going to literally write that algebraic lee and say, X plus two cannot be zero and X cannot be zero, and then we&#x27;ll just solve them both out. 1st 1 we would need to subtract two to the other side. Giving us that X looks like it can not equal negative, too. For the 2nd 1 it&#x27;s kind of already solved out. So our answer is X squared plus three x minus four over X Times X plus two. Assuming that X does not equal negative too, and X does not equal zero

Problem

In $25-30,$ perform the indicated operations and …

Problem 28 Medium Difficulty

In $25-30,$ perform the indicated operations and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined.
$$
\left(x^{2}-2 x+1\right) \div \frac{x-1}{3} \cdot \frac{x+4}{3 x}
$$

Answer

$\frac{(x-1)(x+4)}{x} ; x \neq 0,1$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Grace H.

Heather Z.

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Absolute Value - Example 1

Absolute Value - Example 2

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$\frac{(x-1)(x+4)}{x} ; x \neq 0,1$

Algebra 2 and Trigonometry

Grace H.

Heather Z.

Caleb E.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Heather Z.

Caleb E.

Kristen K.

Ann Xavier Gantert

Algebra 2 and Trigonometry