write-each-rational-expression-in-simplest-form-and-list-the-values-of-the-variables-for-which-the-3

Question

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined.
$\frac{12 x y^{2}}{3 x^{2} y}$

Bahar Tehranipoor · Accepted Answer

in this exercise, we want to supervise expression and find, with the fractions undefined. So let&#x27;s just starts canceling some things out in the numerator and denominator. So see that we have X and X squares. That means you can take this exile and just haven&#x27;t X. That is to the power of one and the denominator. Then we have a why that we can get rid off and then just make y squared. Why? We also know that 12 and three are both multiples of three. So if we just remove that, we get a four in the numerator. So this got kind of messy. So it&#x27;s rewrite and we have the four left excess appeared before. Why over the three is gone x in no wise, just x. So that is our expression simplified. Now we want to find where is it? Undefined? We go back and look at the original expression and see where with the denominator equals zero. And that would be when X equals zero in y equals zero. So we say that ex cannot equal zero in like Michael zero, because at those points, expression will be undefined

Bahar Tehranipoor · Answer

Ooh, simplify this rational expression and enlisted values, the variables for which the fractures undefined. So let&#x27;s see if we can factor anything out in the denominator. We can see that we have a wide. It&#x27;s common in both terms, and you have an excess common in both terms. We also have three that&#x27;s common in both terms. Let&#x27;s take all this stuff out. We can take out that three x y from both terms. And what are we left with taking three x y out of nine x y over left with his three. We take it out of six x squared y cubed. We have two. The two factors left. We still haven&#x27;t X left and we have a Y Square left and the numerator. We just have that three ex wives I could already easily see that we can divide all these terms out and we&#x27;re left with one over three plus two x y squared. Now, where will this fraction be? Undefined. We just This is the denominator equal to zero. So if we said the denominator equal to zero, we get to X. Why squared plus three equals zero. We sold for this. We get that to x y squared equals negative three. When we say that X Y squared equals negative three over two. And actually we would say Ex Kwai scored cannot equal negative through over to because that would make the fraction to find and going back to the original expression. We see that we also have that factor of three x y that we divide it out when we sell to consider that we have to say that ex cannot equal zero and that why cannot equal zero either. Because even though these aren&#x27;t, they&#x27;re in the simplified expression. If these were true, if we had X equals zero y equals zero, then we would end up with a zero on the denominator and we would have a notify infraction.

Martha Richards · Answer

So we&#x27;re gonna write this rational ex Russian here in simplest forms form, and we&#x27;re also going to provide the value for X here that will make this rational expression undefined. And so the really the easiest thing to do here is to factor both of these so well, factor the top here. So we have, well, excess because the only way when we foil remember to get first to equal X squared as to have extends X and then we look here and we see in order to have a positive but have the addition or subtraction add up to have a negative number is for both numbers to be negative. Um, and then what? We look for us factors of 12. And so here we want factors of 12 that will add up because these are the same sign here to seven. And so that&#x27;s three and four. So I have X minus three times x times for And when I boil this back out, I get back up to there and then in the denominator, the same thing. So I have access. But here I have a negative and positive here, so I have to have one positive and one negative. And then this case, the difference is going to be this term here. And so the only way to get that is a five and a three. So we want the five to be the positive number, because when we, uh when we take the difference, we need the number to be a positive. And so that&#x27;s these two here. So now let&#x27;s take a look at the denominator. And if either one of these zero, then this would be undefined. So that means if X is a negative five or if access a positive three, right, cause three minus three would make that zero, then this would be this rational expression would be undefined. Then let&#x27;s also reduce this so we can cross these guys out. And so what I have left is X minus four, divided by X plus five

Bahar Tehranipoor · Answer

in this question. What we&#x27;re gonna do is we&#x27;re going to simplify this expression, and we&#x27;re also gonna find the values of X where this function just doesn&#x27;t work. And usually how we do that is by look hands don&#x27;t make her go first. Let&#x27;s simplify. So what we&#x27;re gonna do is let&#x27;s just simplify the new writer first. Cool. It&#x27;s just easier to look at. We have four minus. We&#x27;re gonna have negative two times X minus two X and the negative two times negative one. It could be really easy to mess that up and put negative, too. But it&#x27;s actually me plus two. So that altogether comes six minus two x now, and it&#x27;s not. What we want to do is to factor that, because right now we can&#x27;t really see easily what&#x27;s gonna divide into expert my ass. Sex experts nine. But if we factor it, which will be X minus three squared, it&#x27;s easier to see what will divide into that. You can see. Ex ministry will divide into that and look at the new Raider six minus two X if you can catch it. If you multiply a negative to our fear factor that out, we will have negative two times X minus three over X minus three squared. And then if we divide out that, explain the street, we get negative to over X minus three. And now that is going to be the answer. And to find where this function is invalid always to do is say, where&#x27;s is no major zero If X minus two equals zero, that means X equals three. So we sent an ex cannot equal three for this function to be true over all the rest of values, and that&#x27;s it.

Bahar Tehranipoor · Answer

and this question. We want to simplify this expression and we want to find where the fractions undersigned. So first, let&#x27;s factor the numerator and denominator. Looking at the denominator, I think it&#x27;s just easier to dio we get six times. Why times Why the numerator? We can take out a three and a wife so they take out three wives. We have three y into nine. My squares school be three wine and then 3123 wise, just just one. So let&#x27;s divide out what we can do right out so I could disappear. And then with this three and six, we can divide that. So we&#x27;re just left with two. So all together we&#x27;re left with three. Why? Plus one overs We have this through a plus one of the numerator and the denominator. Since we divided out that three, we&#x27;re gonna have to whine. Now, where is this for action? Going to be undefined? Swear the Jin Ah mater equals zero. And that&#x27;s just one Y equals zero. So you see that why not equal zero

Stephen Deluca · Answer

Okay, so for this question here, we&#x27;ve kind of got two parts. Simplify the rational expression and the second part being state. Any restrictions on the variables? So what we&#x27;ll do first is well, look at this top expression on the fraction, and we can see that we have on X and A Y in both of the top terms. So what we&#x27;re gonna do is we&#x27;re gonna factor an X Y out of the top first, and we will get X. Why? And then we&#x27;ll include whatever is left over in the top. So we have a y squared, subtract a nine. No, let&#x27;s look at the bottom of this fraction. And what we notice year is that we have on the bottom three terms. We&#x27;ve got a multiple of 12 that exist in all three of those terms. We have a new axe in all three of those terms as well, so we can factor out a 12 ax so we&#x27;ll go ahead and do that for the bottom of this traction. 12 x and what&#x27;s left over in the first term is going to be a y squared. Plus why minus 12 because 12 times 12 is 1 44 Next. What we want to realize is that on the top of this fraction here, we&#x27;ve gotten accent as well. We&#x27;ve got an X on the bottom of this fraction. And since X divided by X is one, we can actually just cross those two axes out because it was one. The next thing we want to do is we&#x27;ll look at the top section here and we see that we&#x27;ve got Y squared minus nine. And what we&#x27;re going to want to do here is we&#x27;re going to want to factor this into two brackets. So we&#x27;re gonna have on the top of this fraction why there&#x27;s gonna be two brackets that the Y squared minus nine is gonna break up into. Now we know that each bracket is gonna need a why at the front. But to determine what will go for the second part of those brackets. Those two numbers are goingto have to multiply Thio equal the nine or the negative nine and they&#x27;ve got toe add Thio equal zero because here there&#x27;s actually a hidden zero. Why turn? Because this is a try. No meal missing that middle term, so we&#x27;ll figure out. What are the multiples of not our negative nine? We&#x27;ve got one and negative nine. You&#x27;ve got negative one and causes of nine. We&#x27;ve got positive. Three you&#x27;ve got positive three and negative three. And those air all of the multiples that we have. So which one of these combinations add up to zero? Well, that will be this bottom one here, three plus negative three year zero. So we know that the Rockets are gonna have to be three and negative three for that second part here, So we&#x27;ll put in the positive three on the negative three. Now, for this next part, we&#x27;re gonna do the same for the bottom expression for try no meal that&#x27;s in this bracket here and again. What we&#x27;re going to do is we&#x27;re going Thio Keep the 12. We&#x27;re gonna break it up into two brackets. Gonna factor it into two brackets again. We&#x27;ve got the why at the start of the two brackets. But now we&#x27;ve got a negative 12 at the end, so we&#x27;ve got to find a number. There are two numbers that multiply to get negative 12 and add up thio plus one. Why right? Because there&#x27;s only one. Why, that is hidden little one. So what we&#x27;ll do is we&#x27;ll again list e multiples of negative 12. So we&#x27;ve got one. Negative 12. We&#x27;ve got 12. Negative one. We&#x27;ve got three negative four. We&#x27;ve got four negative three. You&#x27;ve got six negative. Too negative. Six. Positive, too. So which one of these add up? Which one of these combinations here add up to you? Positive one. Well, that&#x27;s going to be this one. Here it is. Four plus negative. Three is one. So, again, those are gonna be the numbers that we&#x27;re going to use for. The brackets will have paused before negative three and will notice that on the top, we&#x27;ve got a Y minus three bracket on the bottom. We&#x27;ve also got a Y minus Lee Brackett. And since we&#x27;re dividing those exact same terms, we can just cancel them out because they reduced to one and we&#x27;re left over with the answer being. Why Bracket? Why? Plus three all over 12 bracket. Why? Plus four. So now we&#x27;ve simplified this rational expression. That was that first part to the question. The second part is going to be stating any restrictions on the variables So if we look at our answer and particularly down at the bottom here, if the bottom of this fraction is equal to zero, it is undefined because we cannot divide by zero, uh, and get a solution. So to make the bottom part of this Fraction zero, why would have to be negative? Four. So we can&#x27;t have that. So why cannot equal negative four? Because then we&#x27;ll get zero. There&#x27;s one other restriction, and where we want to find it is back up the original equation. And if we look again at that bottom denominator of the fraction, there&#x27;s an ex term now that we had already factored out but exists in the original function. So what we want to do is realize that if X was zero, this whole bottom fraction here would be zero. And we can&#x27;t have that. We can&#x27;t divide by zero and get a defined answer. So x you do that again there X cannot equal. And so these would be the restrictions

Problem

Write each rational expression in simplest form a…

Problem 13 Easy Difficulty

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined.
$\frac{12 x y^{2}}{3 x^{2} y}$

Answer

$\frac{4 y}{x} ; x, y \neq 0$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Catherine R.

Alayna H.

Caleb E.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

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$\frac{4 y}{x} ; x, y \neq 0$

Algebra 2 and Trigonometry

Catherine R.

Alayna H.

Caleb E.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Alayna H.

Caleb E.

Michael J.

Ann Xavier Gantert

Algebra 2 and Trigonometry