brianna-said-that-frac3x-2frac5x2-is-a-rational-equation-but-fracx-23fracx25-is-not-do-you-agree-wit

Name: brianna said that frac3x 2frac5x2 is a rational equation but fracx 23fracx25 is not do you agree wit
Uploaded: 2019-07-31
Duration: 3 min 6 s
Channel: Numerade
Description: Brianna said that $\frac{3}{x-2}=\frac{5}{x+2}$ is a rational equation but $\frac{x-2}{3}=\frac{x+2}{5}$ is not. Do you agree with Brianna? Explain why or why not.

Question

Brianna said that $\frac{3}{x-2}=\frac{5}{x+2}$ is a rational equation but $\frac{x-2}{3}=\frac{x+2}{5}$ is not. Do you agree with Brianna? Explain why or why not.

Dilip Paruchuri · Accepted Answer

Hey, guys. So in this problem were given two sets off. Rational equations are 1st 1 is three over X minus two equals five over experts to and our second equation is X minus two over three equals expose two or five and other problems. States that the student named Briana considers this first set this for a set of equations of rational equation. She considers it a rational equation. However, she does not consider the second equation irrational equation and the textbook and success to, um, verified. Briana is correct, Incorrect and explain why. And in order to understand if she&#x27;s correct or incorrect, we need to understand the definition of a rational equation and a rational function. Rational equations are basically any equations I&#x27;m gonna reviewed here. Rational equations, basically, or any equation when you have two rational functions said equal to each other. And in order to understand what rational functions are, I&#x27;m gonna explain that a bit rational functions functions are any functions such that there&#x27;s a polynomial in either the numerator, the denominator or both. Meaning rational functions are of this four p of X over Q of X. And let&#x27;s take a look at each of these ah functions in both of these equations. Three over X minus two. The reason. Constant function. It&#x27;s a constant polynomial, so it is a polynomial X minus two. Linear. It&#x27;s a linear function. It&#x27;s a polynomial. Similarly, we see the F over five over exposed to sorry is also each each the numerator and denominator of both polynomial tze and weaken Tell that these two these two functions are rational function similarly over here X minus two. Now the function the polynomial is in the numerator still makes it about rational function are exposed to over five also a rational function because you have a polynomial in the numerator and the denominator. And so in both of these equations we have rational functions being set equal to each other. So in reality, both of these equations are indeed valid. Rational equations and Briana is incorrect in Mackey&#x27;s of Briana is incorrect. Rihanna is incorrect. She&#x27;s incorrect, that only the 1st 1 is a rational equation because in reality, taking a look at the definition of rational equations and rational functions, we see that both functions are rash boat by functions. I mean both equations, our rational equations. So I hope that answered the problem and thanks for listening us

Stephanie Galvão · Answer

So here we want to solve this equation. And to do it, we need your first completes the media much Tacoma. And here we have that it is 15 times eggs. So here, I&#x27;m just gonna mooch play these e no terms off the equation. Okay, so here I have 15 x times Chu less Oh, himself Throat 15. Thanks. Times three over five and two over X times 15 x. Okay. And if the women Why here? We can just simply Fine. OK, And here we we will have this and we will have this. Okay. And we will have one and five. So we just simplify the equation and way we were up Tank year. Let me just right here. Um five. Thanks. The times true. Plus three eggs, times three. Okay, it&#x27;s equal to the here. We can just do the multiplication and we will have Tanox plus Nynex. It&#x27;s equal territory. And if we do the some here, we will have 19 x importunate Terry, where X is sorry. Overland him. Okay, so now we can just verified solution. Okay, substituting these in the equation. So here we will have. True to over three. It was tree over five a poor too. Two over 30 Overnighting. And here we can just which by the inverse off the fraction and in to become 19 times two over curry, it will be one 15. And here the minimum which broke Homan is 15. True. So here we have 15 15 divided by tree. It&#x27;s five times shoe you, Stan plus puting developed by five history times 3 19 So it is 19/15. You go chew 90/50. Okay, so it is It is just right here, okay?

Carson Merrill · Answer

so, with his problem, were given another irrational. Another rational equation. X over three X squared plus five x, my ass too minus five over. Exposed to equals Negative one three x over three X minus one. So the best place to go with these rational equations is to figure out a common denominator, and we&#x27;ll see why in just seconds. So to find a common denominator, it&#x27;s really helpful to factor out the denominators as best we can. And so we see that, uh, if we&#x27;re trying to factor this right here, we need to think what multiplies to negative six and adds to five. And we know that this would be negative six or a positive six and a negative one. So let&#x27;s just drop this down, actually. So that tells us that three X squared minus six actually plus six x minus X minus two. Then this gives us three x Times X plus two minus one times X plus. Two says the process. We go through two factor polynomial with a coefficient, um, on the highest degree. And this gives us three X plus or sorry, three X minus, one times exposed to so we can write that right here. So we have three X minus one and X Plus two and a top we Apax. And we had the same thing here and here, but we want the denominators to be the same. So what is going to leave us with is because I already have the X Plus two and we want there to be a three x minus one. We&#x27;re gonna multiply that down here, and then we&#x27;re also gonna multiply it on the top is well, so if we take our five times three X minus one, that would give us 15 X minus five and then this is going to equal three X minus one. We want there to be the X Plus two, though, in order to have the common denominator. So when we have X Plus two, we multiply down here, we&#x27;re also gonna multiplied a top, so that&#x27;s gonna leave us with negative X minus two. So because the common denominator is because they were coming denominator now and it&#x27;s all the same, um, we can now restrict the equation and just look up what we have here. So we don&#x27;t need this anymore. Um, so bringing this down. We have X minus 15 X plus five equals negative X minus two. We can combine like terms will send the five over here and we&#x27;ll send The X is over here on, and that is going to give us a 13 xnegative 13 x and a Let&#x27;s see, that would be a negative seven here and then we divide both sides by negative 13 and we see that X is equal to 7/50. So with X equal to 7/13. Um, we just need to check her answer now. Eso, in order to do this weird is going to input this into our original equation because we are dealing with a fraction. It&#x27;s going to be a lot easier if you use a calculator. And so that is what we will do. So we have three x squared, so it&#x27;s gonna be seven divided by 13. Um, we&#x27;re gonna do three x squared plus five x on the minus two. That will give us around 1.56 on Ben when we divide. When we take the seven over 13 up here again, your calculators will be very helpful for this. Just because we&#x27;re dealing with a lot of fractions and decimals. 15.3, 3.3 four five minus. And then we have five divided by, uh, X plus two. So 70 by 13 plus two and then five divided by that. That&#x27;s a one point nine six 97 And then when we subtract this, we get, we&#x27;re going to it&#x27;s going to come out to be a negative 1.65 That would be the closest we could get to it. Negative 1.625 Actually, that is what that comes out to. And then we see that if we do the same thing on this side right here, we have three times three times 7/13 minus one and then we&#x27;re going to divide. We&#x27;re going negative, one divided by that answer, and that will give us also negative 1.65. So there we checked her answers, and we see that when X is equal to 7/13 it does still check out. So that is our answer

Matt Gibson · Answer

the answers for part A are you multiply the numerator and denominator, and when you do that medication, you would get what we see here for part B to divide, we invert the divisor and then multiply. So if you do that, the three we get multiplied by the X Plus Two and the X Times the X Plus five.

Ankit Gupta · Answer

in this question, we have no check that the solution get by brothers is correct or no. So here, brothers guard the following solution G minus X divided by X minus Fight No. First they used the full infection notice minus one multiplied by X minus tree. Yeah, I did. By minus one. Will de blabber fry minus x no on Cancel the like plums and then simplify. We get X minus tree, multiply by one Do I did by by minus X So here, bigger the same solution as the by the so he got up credit uncertain.

Angela Guo · Answer

we want to determine if five is a solution of give emotional equation. So for this one, all we have to do is pledging five. That&#x27;s five minus one. This is gonna be one minus 3/5 minus. So the left side is 1/4, and the right side is one minus real before which ISS 1/4. So this one is good. Five is a solution who are part to be? If we look at our denominator, we have X minus five. So if we try to put in fi, we get five over five minus five, which is 5/0, and we can&#x27;t divided by zero. So in this case, um, it is not a solution. Um, because we end up dividing by zero.

Problem

In $3-20,$ solve each equation and check. $$ \f…

Problem 2 Medium Difficulty

Brianna said that $\frac{3}{x-2}=\frac{5}{x+2}$ is a rational equation but $\frac{x-2}{3}=\frac{x+2}{5}$ is not. Do you agree with Brianna? Explain why or why not.

Answer

Yes

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