write-each-rational-expression-in-simplest-form-and-list-the-values-of-the-variables-for-which-th-15

Question

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined.
$\frac{5 y^{2}-20}{y^{2}+4 y+4}$

Bahar Tehranipoor · Accepted Answer

and this question. I want to supervise expression and find where it&#x27;s undefined. So let&#x27;s start with factoring the numerator and denominator. But I think the numerator just looks easy to do, so we&#x27;ll take out of five. So we have five times. Why squared minus four. We could factor Weiss. We&#x27;re minus 42 So we have five times. Why? Minus two times why? Plus two. Now the denominator. We can just factor into why. Plus two square. That is why scruples for why I posed for. So let&#x27;s divide out that white clothes, too, in the numerator and denominator and we&#x27;re left with simplified five. Why minus five times I got to so 10 over Why? Plus two. So now we want to find the values of exports under five, and that will be with the denominator equals zero. And the denominator would equal zero if why equals negative too. So we say that why cannot equal now you have to

Martha Richards · Answer

All right. So we&#x27;re asked to simplify this rational expression and also list the values of the variables for which this rational expression would be undefined. So the first thing I would do is find the undefined part, because once these things cancel, you can see these. They&#x27;re gonna cancel here. Then this will no longer have a denominator that cannot be zero. So what we have is is that we can&#x27;t have zero down here. So if 10 a is equal to zero than it is undefined and so then that means just the A equal zero is when this is this rational expression is undefined. And then now we can just redo. So when I have a five and the numerator and attending the denominator both these air divisible by five So this becomes one. And this becomes too. When you have two A&#x27;s above and one below, you can get rid of one and you keep just one, eh? So I&#x27;m left with in the numerator a be over too

Bahar Tehranipoor · Answer

and this question. We want to simplify this expression, and we also want to find where it&#x27;s undefined. So first, let&#x27;s factor the denominator. If we do that, we put in the black worker they go, we get if we take a d l d times 15 minus 20 d, then the numerator. We just still have 10 D. Now we can see that there&#x27;s gonna be a multiple of five in both the numerator denominator. So let&#x27;s take that out. The factor. This we get five times to D and the denominator we have. If we take a five out, we have five times D taking out of 15. We get three minus and then 24. So you have three minutes 40. Let&#x27;s divide out five about the deed. We simplify it and we get to over three minus 40. Now to find with this is undefined. We look for where the dura mater zero in the original expression, So 15 D minus 20 d squared. We&#x27;re going to have the 1st 1 It&#x27;s easy to see is D cannot equal zero because that will have an undefined expression that we can set this denominator equal to zero and we&#x27;ll get that d equals through before where the equal zero. So that d cannot equal three over four because these will give us an owner&#x27;s zero, and that is your superfight expression.

Bahar Tehranipoor · Answer

and this question. Want to simplify this expression? We want to find where it&#x27;s undefined. So first, let&#x27;s fact earthy numerator so we can take out a four. Do that. We&#x27;ll get a squared minus four, and we can also factor this into keep that for a minus two times eight plus two. So usually when you see a term squared minus some constant, it&#x27;s really easy to factor it. And then in the denominator, we can also take out of four, four times eight plus two and we&#x27;ll have overhears and thing. Four times it was two. And now let&#x27;s see what we can divide out. We can divide out that four divide out in April&#x27;s too, and very simply, we&#x27;re left with a minus tube. That&#x27;s her answer. But to find words undefined, we have to look at the denominator of our original expression and see where that will be. Zero. Because the denominator zero, the expression is on the fine. We have four day plus eight equals zero, and if we really quickly saw that, we get that A cannot equal negative too, because then we haven&#x27;t undefined equation

Gladys Fowler · Answer

for Problem number 12. We want to keep in mind that it&#x27;s the same thing. Is problem number 11. So we&#x27;re given an expression why square minus four Y minus five all over. Why squared plus five y plus four. So we want to first simplify our expression. That&#x27;s the first part of our answer. So we need to factor both numerator and denominator so we can use the little trick that I&#x27;ve been using since number one. And we can put our see value in the top and our be value in the bottom. So we need to find two numbers that multiply together to give us negative five while also adding together to give us negative four. So in this case, this is going to be negative. Five and positive. One negative five plus one is negative four and multiply together. It&#x27;s negative. Five. So we just need to split these two up to why, minus five times y plus one all over. We could do the exact same thing to our denominator. And that would be four and five. Well, it&#x27;s actually gonna be very similar. This is gonna be four and one. So four times one is 44 plus one is five. So we split those up to y plus four. And why plus one, we can see that we have a Y plus one in both our numerator and denominator. So we can just cancel those out, leaving us with Y minus five all over. Why minus four? That&#x27;s the first part of our answer to simplify the expression. Now, the second part, it asked us to identify all the values that need to be excluded from our domain. Remember, if you have an expression that looks like this, the only thing that we care about is our denominator, not Equalling zero. If our denominator equal zero, then we haven&#x27;t undefined expression, and that would be something that we would have to exclude from our domain values. So in this case, all we would have to do is take our denominator. Why minus four, and set that equal to zero and solve. We do not care about what&#x27;s in the numerator. That&#x27;s not going to effect whether we haven&#x27;t undefined function or not. So we would add for to both sides and why equals positive four. So the second part of our answer would be why is not equal to four, and I will box adding green as well. And we&#x27;re finished

Amy Jiang · Answer

so it&#x27;s over, noting Internews. Right now we can practice since Y plus for times like this one. And in orange nominator we have lying when it&#x27;s five times Why, um, plus one. And now we can&#x27;t go out this white close one. So we&#x27;re left with a Y plus four overline minus five for our solution.

Problem

Write each rational expression in simplest form a…

Problem 25 Medium Difficulty

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined.
$\frac{5 y^{2}-20}{y^{2}+4 y+4}$

Answer

$\frac{5(y-2)}{y+2}$
$y \neq-2$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Heather Z.

Alayna H.

Maria G.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

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$\frac{5(y-2)}{y+2}$$y \neq-2$

Algebra 2 and Trigonometry

Heather Z.

Alayna H.

Maria G.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Heather Z.

Alayna H.

Maria G.

Kristen K.

$\frac{5(y-2)}{y+2}$
$y \neq-2$

Ann Xavier Gantert

Algebra 2 and Trigonometry