in-25-30-perform-the-indicated-operations-and-write-the-result-in-simplest-form-in-each-case-list--2

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.
$$
\frac{3 x}{x-1} \cdot \frac{x^{2}-1}{x} \div \frac{x+1}{3}
$$

Alisa Lu · Accepted 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 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, 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.

Derrick Hanson · Answer

So with this one, we&#x27;ve got three different pieces here. Now, My 1st 2 fractions here. Nothing wrong with these two. That&#x27;s just a straight of multiplication problem. We could go ahead and do that right automatically if we wanted to, but I do have this division right here. Okay, We know how to mess with division problems. The way we do that is we change the division multiplication by flipping the second fraction. Well, in this case, technically, it&#x27;s my third fraction. But I&#x27;m looking at just this division problem right here. If we&#x27;re looking at just that division problem, we&#x27;ll just rewrite the 3/5 and then for my division problem year, the first part 5/9 will stay exactly the same. We keep that the same. The second part of my division problem. The second fraction involved in my division problem that is the one that we will need to flip or find the reciprocal of so that we can get everything back to multiplication once we&#x27;ve taken care of that. Now we can go finish the rest of this by factoring each numerator and denominator separately and then seeing what can simplify cross out All right, so three is just three. There&#x27;s nothing really to do with that. Five is just five. There&#x27;s nothing really to do with that. Same with the numerator. 59 Finally, something we can factor nine breaks down into three times three and then three is just a three. Four can break into two times two. And now we&#x27;re going to see what we can cancel out. Remember what? Every time we cancel any numerator that matches with any denominator can cancel meeting this three in the numerator could cancel with this three. And the denominator this three in the numerator could cancel with this three in the denominator, this five in the numerator could cancel with this five in the denominator. I don&#x27;t see anything else that matches up between the numerator and the denominator, mostly because I&#x27;ve gotten rid of all our enumerators. If we can&#x27;t sell out everything in the numerator ordered on there, we&#x27;re left with just a one. In my denominator, I am left with two times two, which would be four. So it looks like our final answer is 1/4. No variables here, so no need to do any more work as faras undefined values

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.

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.

Problem

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

Problem 26 Hard 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.
$$
\frac{3 x}{x-1} \cdot \frac{x^{2}-1}{x} \div \frac{x+1}{3}
$$

Answer

$9 ; x \neq 0, \pm 1$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Grace H.

Catherine R.

Kayleah T.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

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$9 ; x \neq 0, \pm 1$

Algebra 2 and Trigonometry

Grace H.

Catherine R.

Kayleah T.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Catherine R.

Kayleah T.

Caleb E.

Ann Xavier Gantert

Algebra 2 and Trigonometry