Solving a rational equation with two solutions

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👉 Learn how to solve rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational equations, one of the ways is by multiplying all the individual rational expressions by the lowest common multiply (LCM) of the denominators. This eliminates the denominators and then we can evaluate the resulting equation accordingly.
It is very helpful to check your results by substituting them into the original equation to see if they are true. This also helps to identify the extraneous solutions. An extraneous solution is a solution that is obtained during the course of solving an equation but which does not hold true for the original equation.
Timestamps:
0:00 Intro
0:26 Start of Problem
Corrections:
5:16 It is positive 6x, not 2x.
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✅ How to Solve Rational Equations
• How to Solve Rational ...
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✅ How to Solve Rational Equations with Monomials
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✅ How to Solve Rational Equations with an Integer
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✅ How to Solve Rational Equations | Learn About
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✅ How to Solve Proportions with Trinomials
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Опубликовано:

15 июл 2024

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Комментарии : 251

@fernandadiaz3024 6 лет назад

i'm in college and still look to you when I don't understand my professor, awesome job, your students are very lucky to have you!

@brianmclogan 6 лет назад

happy to still be able to help you out!

@jre011 5 лет назад

Let me get your snap cutie

@benlee5039 5 лет назад

@@jre011 creep

@bmshadmansakib1142 3 года назад

But sometimes it is very hard to understand but from the beginning to intermediate I understand

@bmshadmansakib1142 3 года назад

Then I get confused at later

@alwaysnelsontacos2903 5 лет назад

Why he got to call out Danielle like that

@aaryonaadams7414 4 года назад

She probably was doing something she wasn't supposed to be doing. I know because of experience lmao!

@JohnDoe-hq1qx 4 года назад

ye, teachers usually do that to get their student's attention

@garycook6344 4 года назад

I am a Dad trying to help his son understand solving rational equations. I am having to learn this all over again. This video was very helpful. Your students are lucky to have you. I will undoubtedly watch it a couple more times.

@sumangilchristinekyle8086 6 лет назад

That student shocked me lol hahaha

@brianmclogan 6 лет назад

how?

@liiqmariie 6 лет назад

YOU SUCK very weird how that is still shocking to some crazymusicgrl

@crazymusicgrlcheesecake 6 лет назад

just yesterday a white woman gasped when she saw me walking pass her. omg these people are ridiculous. If I wasnt on duty I would have make a remark. 😂

@eileen3116 6 лет назад

What? lmao

@lightryuzaki3974 5 лет назад

Wtf!.......hahaha

@novie7945 3 года назад

Brian, I don't know if you read comments on old videos, but thanks to the pandemic, taking online classes has meant a lot of struggle. Currently I'm in a class that doesn't have much in the way of video supplementary material, and I can't tell you how much all your hard work has helped me passing my tests this quarter (even if it's by the skin of my teeth!)

@Yirukai 5 лет назад

Preparing for the GMAT. These videos are pure gold to me. Thank you so much Brian.

@jennifersmith-colton8806 5 лет назад

Holy hell. I've been stuck on this one concept and FINALLY, a video I can follow 😅😅.

@UrtleMnL 3 года назад

Wow, this is super useful! Even though I'm not in your class, I get a whole explanation of everything as if I was there!

@JosiahHenry7 4 года назад

Isn’t it crazy how this video is still of use? Thank you so much! Big test coming up tomorrow!

@jamesh8163 6 лет назад

Well looks like I'm failing tommorow

@brianmclogan 6 лет назад

you got this

@VictoriaSays 5 лет назад

OMG lol

@victoriamercado960 3 года назад

It’s ok cause I failed today lmao

@dahlia5233 3 года назад

The best math teacher award must goes to you 🥺 Thank you for helping!

@dmc_9894 4 года назад

damn... i really really needed this.. i have a midterm in my 118B math class tomorrow and i didn't fully understand how to setup like this.. thank you!!!!

@derixpop56 4 года назад

total lifesaver...Thanks for posting!

@som_girl6702 3 года назад

one is also a denominator that should have been among the LCD products. It's easier for anyone learning to find LCD to know that no denominator should be eliminated until they fully understand that one multiplied by any number is that number and can be ignored when finding LCD if it is a denominator. Great video!

@User-mt4ed 5 лет назад

It is the exact question I had in my book and this video helped me a lot to do my maths revision

@notimportant5894 6 лет назад

very helpful for a test coming up!

@brianmclogan 6 лет назад

awesome! best of luck

@jujukelkel 3 года назад

2021 here! Exam on this stuff tomorrow. I'm glad I found your videos!

@roxyqueen5076 6 лет назад

Great !!! TEACHER!!!! I wish I had you when I was coming up in my high school years..all my teacher did was sleep or read my freshman year..seriously u r truly awesome!!

@brianmclogan 6 лет назад

happy to be there for you Roxy.

@truthobservatory6767 5 лет назад

Holy shit i figured it out god bless you

@brianmclogan 5 лет назад

Happy to be there for you :)

@bellajoslin8374 5 лет назад

This really helped me. Thank you!

@amayalopez4602 5 лет назад

this was super helpful. thank you!

@Natasha-th7bb 6 лет назад

Thank you so much! Your teaching is great :)

@brianmclogan 6 лет назад

happy to help

@HEREandNOW310 5 лет назад

This works for me. Thanks professor

@thealareza3666 3 года назад

2020 still learning a lot from you .

@CJamesEA 3 года назад

Thank you so much Mr. Brian

@palermogaas480 3 года назад

very clear discussion :) thanks sir.

@J03L157 5 лет назад

really helped! thank you

@BlueCJ 2 года назад

Thank you so much for this, the videos that were sent to us didn't help me that much so I appreciate this!

@jordenhilbink5543 5 лет назад

Omg this video actually helped me understand all praise this man.

@whitediamond0407 10 месяцев назад

Easy, Thank You.🙏🏻

@alexgarcia8519 4 года назад

Y’all this mans just blew my mind

@juhbulis559 4 года назад

2:46 was a jump scare dude I thought I was getting taught math not pooping my pants

@jacksonjohnson9674 Год назад

2:43 "sup?!" 😂

@liam7752 5 лет назад

Thanks this was very helpful

@Shelby58085 6 лет назад

Thank you! This was very helpful!

@brianmclogan 6 лет назад

you are very welcome!

@frncsldd8236 5 лет назад

We are the students in 0:43

@yeetthemeat3853 3 года назад

Thanks for sharing the video.

@escobar8617 6 лет назад

thank you sir you are exellent!

@brianmclogan 6 лет назад

happy to help

@afiyaparveen2864 5 лет назад

Thanks a lot you always help me 😇😇😇.

@dusteencerita6263 3 года назад

Sir? Do we always transpose the right part of the equal sign on the last, to the left?

@freddiemarien 5 лет назад

your videos go a long way out. thanks for the help

@brianmclogan 5 лет назад

Appreciate it. Thanks

@cxlebproductions4686 5 лет назад

i kept tryna find the one part where the student got up its 2:46 youre welcome haha and thx for the help hopefully ima pass tmrw

@litonkhan6198 6 лет назад

i love your class sir specially your attitude

@brianmclogan 6 лет назад

thank you! happy to help

@somebodysombody5461 3 года назад

This guy really out here saving my gpa

@djaynekalambayi4466 6 лет назад

you are a good teacher.

@brianmclogan 6 лет назад

thank you!

@dilshanisuranga6103 5 лет назад

That guy tells the story about the' kind' of students you were teaching. Nevertheless a very good explanation.

@jordancruz6394 5 лет назад

A very well explain :>

@marz8386 2 года назад

"It can get kinda confusing with dealing with all the different numbers here" Couldn't have said it better myself

@heidirodriguez1093 5 лет назад

I'm about to fail the math portion on the teas test..I know it. I feel like I had it until he started factoring out everything in his head at the end. LOL!

@behzadramandi8818 3 года назад

@Brian McLogan Thanks for the video, Sir, but the correct answers for X are X= -2 and X=3/2. If you go back to your video you'll see where the mistake comes from. Right after factorization when you broke the equation into two parentheses the correct form should be (2X-3)(X+2) but you put it as (2X+3)(X-2). In other words, the way you put it we would have 7X and not (-1)X. Thank you!

@kaitlynclevenger9750 Год назад

bro thank you for commenting this because i really thought i was crazy for an hour tryna figure this out

@nathanli9987 Год назад

@@kaitlynclevenger9750 actually brian is right, if you use "magic X" method factoring out (2x^2-x-6) you will get (2x+3)(x-2) you can watch nancyPi's youtube videos about how to use "Magic X". i assum you just multiplyed -3 and+2=-6, addition, then it will give you -1 but you forget 2x^2 still there.

@user-ky5dy5hl4d 6 месяцев назад

The correct answers are x=-1, x=2. If you have x=3/2 and by pluging 3/2 in 3/2 - 1 that will give you -1/2 and the whole right sie will be negative and that will not equal the left side of the equation. x=-1 is extraneous.

@johnnolen8338 3 года назад

Mr. McLogan, I recently became ensconced in a flame war over a comment I made on one of your videos over six months ago. In the meantime I have been inundated with recommendations for tutorials on how to solve rational equations, as if I needed the help. Not to take anything away from your teaching, the method that you demonstrate here is entirely correct. Nevertheless, there is a more efficient way to solve such problems. If you have a proportion (a rational equation) of the form a/b = c/d then a*d = b*c. This is true because multiplying the original proportion by b*d on both sides of the equals sign such as b*d*a/b = c/d*b*d, yields a*d = b*c; this result is always true. Hence for the equation in question: 6x/(x+4) + 4 = (2x+2)/(x-1), we can first find a common denominator for the terms on the left hand side: [6x + 4(x+4)]/(x+4) = (10x + 16)/(x + 4). Substituting this expression for the original left hand side we obtain, (10x+16)/(x+4) = (2x+2)/(x-1). The foregoing theorem guarantees that (10x+16)(x-1) = (2x+2)(x+4). FOILing both sides gives 10x^2 +6x -16 = 2x^2 +10x +8. Moving all terms to the LHS, 8x^2 -4x -24 = 0. Factoring this quadratic equation gives 4*(x-2)*(2x+3) = 0. This yields the solution set {-3/2, 2}, the same as your method.

@luisa_4120 5 лет назад

damn that student scared me 😂😂😂🤭

@mdeneee1149 5 лет назад

Thank you!!!!!!!!!

@brianmclogan 5 лет назад

You are very welcome

@muscleman2578 6 лет назад

Omg this video is so helpful. Thanks for making this vid

@brianmclogan 6 лет назад

you are very welcome! happy to be able to help you out!

@freeloadph2031 6 лет назад

Thanks💕For Good Teaching

@brianmclogan 6 лет назад

you are very welcome!

@krystalsharvyagapito232 3 года назад

thank you very much

@BilalHub69420 4 года назад

Assalamo alikum sir please explain congruence and similarity

@ShahidBinYasin 3 года назад

Great sir

@JordanDcruz 3 года назад

your students are so goddamn lucky to have you id kill to have u as a teacher

@masterdoughwhale4195 Год назад

thanks you so much for this.

@tubeprincessamirahtv7993 6 лет назад

Do you do this for this equation= z +8/ 6 = 2z+12 /9 - 4z/9 or is there a video for this if different?

@brianmclogan 6 лет назад

same process but the video is more complex. you will want to multiply everything by the common denominator of 9 and 6 to eliminate your fractions

@melanchoolliley 2 года назад

I'd love to be your student ❤️ thankyou!

@limberx128 Год назад

Thanks, teacher

@wh00lio 2 года назад

2:46 made me focus more idk why LOL

@sarahmackavich5551 6 лет назад

Thanks for helping clear up my confusion with LCD.

@brianmclogan 6 лет назад

you are welcome!

@citlaligomez3984 4 года назад

2:47 that kid scared the shit outta me

@thesistersadventures9970 6 лет назад

Thanks this helped alot :)

@brianmclogan 6 лет назад

you are very welcome! happy to be able to help

@gabrielleseru7945 4 года назад

Just curious whos on ur pfp?

@VictoriaSays 5 лет назад

Danielle is in trouble lol

@reainocando241 3 года назад

U really help me thank you muah

@user-ld5ss6pb3u Месяц назад

I am a student and this is in my final When you multiply numerator you also multiply the denominator so what are you doing can you explain

@DylanPirlant Год назад

the kid that came out of nowhere tho

@osbornmanabat8662 6 лет назад

Thanks for tutorial. But I dont really understand what you did in 5:53 - 6:03. Is it the same way of combining all the like-terms on one side?

@brianmclogan 6 лет назад

that is correct, once I have the expression equal to zero I can solve for x by factoring

@osbornmanabat8662 6 лет назад

Can u tell me how to do your own method

@brianmclogan 6 лет назад

not sure what you mean, you understood my process correctly and I clarified it in my comment

@mr.toffee8705 Год назад

8:07 Wait hold on, that should be - 3 & + 2, because if you add 3 and - 2, that would be + x, but given the - x, the greater number should be negative, which is - 3….

@nathanli9987 Год назад

you have to include the 2x^2 too. use "magic x" method facting out the (2x^2 -x -6)

@noah911 5 лет назад

Youre a legend

@brianmclogan 5 лет назад

just happy to be able to help

@12degreesnowman11 Год назад

I was having trouble on these. Simply put, find the LCD

@maxstar557 4 года назад

what level and grade is this targeted to? and what age is this for?

@emmab2767 3 года назад

If I have an equation with two solutions can I choose using only one of them? Or do I have to write both of them?

@Supermax2206 2 года назад

If any of the solutions make the original equation have an undefined variable DONT use it but if neither of them make it undefined then use both.

@jessnam 5 лет назад

that kid scared the shit outta me

@11stem2fadroitnessgom-os2 Год назад

2:45 man that scared the shit out of me

@brianmclogan Год назад

Haha

@skullcandy15151 4 года назад

Good teacher, just sad he has the worst students lol. High schoolers smh😂

@venessakudashkin8038 3 года назад

I have a question, what grade level is this math taken? I finished high school and have never seen my teachers teaching this type of equation.

@andrewjolly319 3 года назад

In the UK you do it at GCSE or about age 14/15

@bruke52 3 года назад

you saved me

@essenceofmagi6416 6 лет назад

I can’t understand this stuff for the life of me... My brain just won’t do it :c

@brianmclogan 6 лет назад

do you have a question?

@essenceofmagi6416 6 лет назад

It’s not a specific question in particular, I just can’t understand any of this for the life of me. Thankfully I’m past it in class but I’ll be sure to revisit this video when it comes time for finals c:

@freddymendoza9393 6 лет назад

College Algebra ain't got nothing on me with the help of Logan lol.

@brianmclogan 6 лет назад

you got this!

@uhmmm1994 6 лет назад

sooo wait, you directly use the denominator as lcd?

@brianmclogan 6 лет назад

well not always least "COMMON" denominator I have other examples where you have to factor the denominators first

@ariannecantor6140 3 года назад

7:35 is it not (2x-3)(x+2) ??

@aiking7357 3 года назад

thats what i was thinking

@mckayludwig2126 3 года назад

Yes, ur right, he also forgot to distribute that 4. That 4 is just Disappear like nothing to worry abouts. Lol

@gibsonj338 4 года назад

0:31 Don’t you mean you have x+4 and x-1 instead of x+4 and x-4?

@aimeecavazos5509 5 лет назад

Your videos ALWAYS help me. When I have money I'm going to buy some merch! #brokecollegestudent Thank you for your awesome videos.

@twitzr5369 5 лет назад

Brian wish me luck tomorrow

@brianmclogan 5 лет назад

you got this!

@ABCDEFG-lj9hv 4 года назад

Tf 5:17 how did that become -2x i thought it was 6x Edit: Nvm he noticed his mistake I didn't watch the whole video yet when i commented

@Shinedown6479 5 лет назад

All that work for 1 answer these are tedious more than hard for me

@djaynekalambayi4466 6 лет назад

👍

@brianmclogan 6 лет назад

cheers

@danishilin8460 4 года назад

smart teacher dome student's

@danishilin8460 4 года назад

@buddafi 5 лет назад

12!

@mfustafaamed2556 5 лет назад

جميل

@ForHimCreations Год назад

What if there are three fractions?

@dgarza421 6 лет назад

Great instruction, but unfortunately I think some of your students haven't learned how to multiply yet...

@brianmclogan 6 лет назад

haha probably true

@yuri4416 5 лет назад

Correct me if I'm wrong I would kindly appreciate it. On 7:15 isn't that supposed to be (2x-3)(x+2)? So your x should be x=3/2 and x=-2. Nonetheless, thank you for giving us students videos to understand it much better.