write-each-rational-expression-in-simplest-form-and-list-the-values-of-the-variables-for-which-the-9

Question

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined.
$\frac{10 d}{15 d-20 d^{2}}$

Bahar Tehranipoor · Accepted 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.

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

Martha Richards · Answer

to write this expression here and simplest form, as well as provide the values for these variables. In this case, only a where this rational expression would be undefined. And so that means that the denominator would be equal to zero is when this would be undefined. So we just sat three a plus 15 equal to zero and Saul. So I subtract 15 from both sides, and then I divide by three, and I get that a is equal to a negative five would lead to this expression here being undefined. And then let&#x27;s produce this. So up top I see that I can pull out a two and I have a A plus five and then in the denominator, I have a three I can pull out, and I&#x27;m left with an A plus five. So these cancel out and I&#x27;m left with 2/3

Martha Richards · Answer

All right, so we&#x27;re giving this rational expression and were asked to reduce it or put it into simplest forms, as well as provide the value for be when that would make this rational expression undefined. So we&#x27;ll start with the denominator, and we will set that equal to zero, because whenever a denominator a zero that would make it undefined. So here, setting this equal to zero adding 16 to both sides gets me B squared is equal to 16. I take the square root of both sides, and I get B is equal to remember. You have to put that plus and minus here four. And so when b is equal to plus or minus four, this leads to this rational expression being undefined. And then what we&#x27;re gonna do now is, uh, sort of multiply this guy out and reorganize and then factor the denominator. So I&#x27;ll start by multiplying out this five to what&#x27;s in parentheses here. So five times one would be five minus five B plus 15. And now what I see here is this five in this 15 ca nbi put together. So I have plus 20. Now I&#x27;ll put out the negative pull out the negative five and I get B plus. Oops. Could be a B minus for because when I multiply this back out, I&#x27;ve got to get a negative times Negative would get me back to a positive and then the denominator here when I have a perfect square and a perfect square with no middle term in a negative sign here, Then this becomes a B plus four times of B minus four, and we can see that these B minus four is cancel and I&#x27;m left with a negative five over B plus four.

Bahar Tehranipoor · 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

Bahar Tehranipoor · Answer

want to write this rational expression and symbols form and then lets the values of variables for which distractions undefined. So very simply here we have six over 10. And because this is independent of any variable, always to do to simplify it is just take out the common multiples that has. So we have six, which we can write as three times two and we have 10 which we can write us five times to getting rid of the twos. We can simplify this completely as three over five, and now there are no values for any variables where this expression will be undefined because it&#x27;s not dependent on any variables.

Problem

Write each rational expression in simplest form a…

Problem 19 Medium Difficulty

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined.
$\frac{10 d}{15 d-20 d^{2}}$

Answer

$\frac{2}{3-4 d}$
$d \neq 0, \frac{3}{4}$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Grace H.

Anna Marie V.

Kayleah T.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

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$\frac{2}{3-4 d}$$d \neq 0, \frac{3}{4}$

Algebra 2 and Trigonometry

Grace H.

Anna Marie V.

Kayleah T.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Anna Marie V.

Kayleah T.

Caleb E.

$\frac{2}{3-4 d}$
$d \neq 0, \frac{3}{4}$

Ann Xavier Gantert

Algebra 2 and Trigonometry