simplify-each-complex-rational-expression-in-each-case-list-any-values-of-the-variables-for-which-11

Question

Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.
$\frac{4 y-\frac{1}{y}}{y-\frac{1}{2}}$

Leina Wu · Accepted Answer

I got in this question. We have a Russian expression to simplify or why one is one of a Why divide by. Why miners? One hot. Okay, so in this expression, we know that there are two fractions. One of the why can one have so in order to get us? Let us simple by this when you to get rid of the one of a why anyone half. So what we can do here is we can mold by the top and bottom by the least, a common denominator. With these two directions the one of a lie in a one path, the least a common denominator will just be to white. So I wore my everything by two. Why? Once you do this, we can distribute the to y to the top, and we can also distributed to wind to the bottom. So if you have distributed to a while on the top, we have four white times to wind. That&#x27;s eight wines square minus one of the White Times to white in the bottom. We have wired times to white, which was two y square, one of 1/2 times to what? Okay, So we had have eight y square, minus two on the top. Because why and what can be reduced in the bottom two and two could be reduced. So you have to Wai Square minus what I keep going. Let&#x27;s see how we can. Some providers on the top We noticed that there was two and eight, so I can factor other, too. I have four wives square miners in the bottom noticed that there&#x27;s why and why. So you can fact all the why and I get e to Why miners What? Okay, now those four Wife square could be further factored as two y plus one and two wine minus one. The denominator you have. Why two y minus one? So we can see over here they have a common factor to Wyman is one that could be reduced. So eventually we have on our final. The answer will be two times two y plus one, too. Bye bye. But now let&#x27;s see what kind of value that why cannot be in terms of the y value, we should look at the original fracture. Original correction is for why to try one of the one divide by wine lines 1/2 so notice that there is one of a why so why can obviously wrote being at the denominator of that fraction. Also, Wyman is 1/2 cannot be zero but that tell us why cannot be zero and why it cannot be one house. So why cannot be zero and one house, and the expression can therefore be simplified as two times two y plus one over why?

Georgiann Andersen · Answer

you really look 12 we&#x27;re gonna simplify this and also determine what value why cannot be we have y plus one house all over to why Plus one, This is the same as saying to why plus one over two multiplying by the reciprocal to why that&#x27;s one. We can cross these out across reduction and we end up with one house. So we&#x27;ve simplified that. Now, when you look at this, the why is not going to cannot be a negative 1/2. And that being, if you set to why plus 1 to 0, you&#x27;re gonna have to y equals negative one, and why is gonna be a negative one hat? So that cannot be why?

Georgiann Andersen · Answer

we&#x27;re gonna simplify a complex expression. And this is number 18. And our expression is one plus one over. Why minus six over y squared. And this is all over one plus 11 over. Why? Plus 24 over y squared. First thing we need to do is simplify the numerator. So if we have one plus one over why minus six over. Why, Square, We need to get everything that has the common denominator of y squared. So we&#x27;re gonna turn the one in tow. Why? Square over y squared? Plus why? Over y squared minus six over y squared. This is gonna end up equaling y squared. Plus why minus six. All over. Why, Squirt? Now we&#x27;re gonna do the same thing. The denominator. We&#x27;re gonna simplify that one too. So we have one plus 11 over. Why? Plus 24 over. Weiss Quirk. We need to put everything over. Why Square? So it&#x27;s why squared over y squared. Plus 11. Why are 11 why? Over why plus 24 over Weiss Court. That&#x27;s gonna leave us with y squared. Plus 11. Why? Plus 24 all over. Why squared? Okay. So we can go ahead and substitute this in. So we have y squared. Plus why minus six all over. Why Square we can multiply that by the reciprocal. So we&#x27;re gonna change it Toe y squared over. Why squared? Plus 11. Why plus 24. We can cancel the y squared, and we&#x27;re gonna end up with y squared. Plus why minus six. All over. Why squared plus 11. Why? Plus 24. Now we&#x27;re gonna factor these out. Why squared? Plus, why minus six is gonna factor out to be a why, Plus three times why minus two. This is all over. Why? Plus three And why? Plus eight, we can cancel these out because there factors in both of them. That&#x27;s gonna leave us with why, minus two over Why? Plus eight. And that&#x27;s as far as you can go. So that&#x27;s your simplest form. Now, if you look at the beginning, why cannot be zero? Because that&#x27;s gonna turn those into undefined fractions. Why cannot be a naked of three, and why cannot be a negative eight

Georgiann Andersen · Answer

Okay, we&#x27;re gonna do to problem number four. We have two fists all over for we&#x27;re gonna simplify this. This is the same as saying to this divided by or when you divide. It&#x27;s the same as multiplying by the reciprocal. And when you multiply fractions, you take the top. The numerator is by each other and the denominators times each other. This is gonna leave us as to over 20. We can reduce that down to one over 10 and that&#x27;s our answer.

Leina Wu · Answer

okay. In his question, we&#x27;re simplifying a fraction to minus two over D over one over D minus one. So when we&#x27;re simplified this weekend, tickle cats, the fractions aimed this conference fraction here to over the e and one day and notice that they all have the d e in the denominator so we can multiply by the common denominator d both on top and bottom. And once we divest, we can to simplify this too. Um, distribute the state we have to de Mona&#x27;s to other D Time state the vibe I won over d Times Day minus one times. So by distributing the d to the open pregnancies, then we have to de monies to end of all right one minus two. Not noticed that the to t minus two on the top you can factor after two. So I&#x27;m gonna fact out to Steve. Miner is one in the bottom. You have one. Run the state and for the demon is one in a woman s t. I can write. The demon is one as negative one times one line. It&#x27;s deep just by flipping the order. But tonight by one ministate, one minus t. When the status on when the requirement is that it&#x27;s fired. This woman is we could be reduced. So we get negative to asked a simplifies dancer. But when we&#x27;re doing this, we haven&#x27;t pay attention to when this would be a ballot. So for De de cannot be a certain value, not just look at this original extraction to over prior to Manistee over one over T minus one. So we know that he is in in the bottom, so he cannot be zero. And for this woman isn&#x27;t demon is one. It&#x27;s in the denominator of distractions. A woman is d minus one cannot be zero, which tell us one Mona&#x27;s de cannot be won and do you cannot be won. So with these two information in mind, we know D cannot be zero and positive. That&#x27;s synthesis. The problem

Leina Wu · Answer

okay. This question were still will find this fraction on type is 1/6. Close. One home for and in the bottom is 1/3 plus 1/2. So if you want a simplified us, we can first of all, observe all the fractions and all of the denominator. We have six for three and two bullets. Identify the least a common denominator. Uh, was 643 to the least commented on merit Could be well, so I&#x27;m gonna multiply everything on top and about by positive love. So once you multiply by 12 we can&#x27;t distribute just 12 into 16 times 12. That&#x27;s gonna be too. And we have looked my one force by 12 the other three to bottom 1/3 times 12 that is for and one have times 12. That is six. We have five over time. 5/10. We can further reduced by side. You get one house. 1/2 is gonna be the simplified form of this fresh

Problem

Simplify each complex rational expression. In eac…

Problem 13 Hard Difficulty

Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.
$\frac{4 y-\frac{1}{y}}{y-\frac{1}{2}}$

Answer

$\frac{2(2 y+1)}{y}, y \neq 0, \frac{1}{2}$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Catherine R.

Alayna H.

Kayleah T.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

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$\frac{2(2 y+1)}{y}, y \neq 0, \frac{1}{2}$

Algebra 2 and Trigonometry

Catherine R.

Alayna H.

Kayleah T.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Alayna H.

Kayleah T.

Caleb E.

Ann Xavier Gantert

Algebra 2 and Trigonometry