Solving a rational equation with two solutions
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- Опубликовано: 23 июл 2024
- 👉 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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#rationalfunctions #brianmclogan
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!
happy to still be able to help you out!
Let me get your snap cutie
@@jre011 creep
But sometimes it is very hard to understand but from the beginning to intermediate I understand
Then I get confused at later
Why he got to call out Danielle like that
She probably was doing something she wasn't supposed to be doing. I know because of experience lmao!
ye, teachers usually do that to get their student's attention
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.
That student shocked me lol hahaha
how?
YOU SUCK very weird how that is still shocking to some crazymusicgrl
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. 😂
What? lmao
Wtf!.......hahaha
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!)
Preparing for the GMAT. These videos are pure gold to me. Thank you so much Brian.
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!
Isn’t it crazy how this video is still of use? Thank you so much! Big test coming up tomorrow!
Well looks like I'm failing tommorow
you got this
OMG lol
It’s ok cause I failed today lmao
Holy hell. I've been stuck on this one concept and FINALLY, a video I can follow 😅😅.
very helpful for a test coming up!
awesome! best of luck
The best math teacher award must goes to you 🥺 Thank you for helping!
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!
It is the exact question I had in my book and this video helped me a lot to do my maths revision
total lifesaver...Thanks for posting!
Thank you so much! Your teaching is great :)
happy to help
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!!!!
This really helped me. Thank you!
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!!
happy to be there for you Roxy.
this was super helpful. thank you!
Sir? Do we always transpose the right part of the equal sign on the last, to the left?
2021 here! Exam on this stuff tomorrow. I'm glad I found your videos!
Holy shit i figured it out god bless you
Happy to be there for you :)
This works for me. Thanks professor
very clear discussion :) thanks sir.
Thank you so much Mr. Brian
2020 still learning a lot from you .
Easy, Thank You.🙏🏻
really helped! thank you
Thank you! This was very helpful!
you are very welcome!
Omg this video actually helped me understand all praise this man.
Thanks this was very helpful
2:46 was a jump scare dude I thought I was getting taught math not pooping my pants
Thank you so much for this, the videos that were sent to us didn't help me that much so I appreciate this!
Thanks a lot you always help me 😇😇😇.
i love your class sir specially your attitude
thank you! happy to help
thank you sir you are exellent!
happy to help
Y’all this mans just blew my mind
Thanks for sharing the video.
you are a good teacher.
thank you!
Omg this video is so helpful. Thanks for making this vid
you are very welcome! happy to be able to help you out!
2:43 "sup?!" 😂
Do you do this for this equation= z +8/ 6 = 2z+12 /9 - 4z/9 or is there a video for this if different?
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
thanks you so much for this.
your videos go a long way out. thanks for the help
Appreciate it. Thanks
A very well explain :>
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
thank you very much
This guy really out here saving my gpa
damn that student scared me 😂😂😂🤭
Thanks💕For Good Teaching
you are very welcome!
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!
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
Thank you!!!!!!!!!
You are very welcome
Thanks, teacher
That guy tells the story about the' kind' of students you were teaching. Nevertheless a very good explanation.
@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!
bro thank you for commenting this because i really thought i was crazy for an hour tryna figure this out
@@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.
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.
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?
that is correct, once I have the expression equal to zero I can solve for x by factoring
Can u tell me how to do your own method
not sure what you mean, you understood my process correctly and I clarified it in my comment
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?
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.
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.
what level and grade is this targeted to? and what age is this for?
Thanks this helped alot :)
you are very welcome! happy to be able to help
Just curious whos on ur pfp?
"It can get kinda confusing with dealing with all the different numbers here"
Couldn't have said it better myself
U really help me thank you muah
I'd love to be your student ❤️ thankyou!
Thanks for helping clear up my confusion with LCD.
you are welcome!
We are the students in 0:43
Great sir
Assalamo alikum sir please explain congruence and similarity
your students are so goddamn lucky to have you id kill to have u as a teacher
2:46
made me focus more idk why LOL
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.
In the UK you do it at GCSE or about age 14/15
Danielle is in trouble lol
sooo wait, you directly use the denominator as lcd?
well not always least "COMMON" denominator I have other examples where you have to factor the denominators first
Youre a legend
just happy to be able to help
2:47 that kid scared the shit outta me
the kid that came out of nowhere tho
7:35 is it not (2x-3)(x+2) ??
thats what i was thinking
Yes, ur right, he also forgot to distribute that 4. That 4 is just Disappear like nothing to worry abouts. Lol
I was having trouble on these. Simply put, find the LCD
Your videos ALWAYS help me. When I have money I'm going to buy some merch! #brokecollegestudent Thank you for your awesome videos.
0:31 Don’t you mean you have x+4 and x-1 instead of x+4 and x-4?
I can’t understand this stuff for the life of me... My brain just won’t do it :c
do you have a question?
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:
What if there are three fractions?
3:54 yooo is that a fucking punnet square, how is science applied to this topic lmao
pretty sure science stole it from math
@@brianmclogan im sorry for my language sir, idek youll reply. And yeah i think science stole it from math.
no worries, cheers!
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
2:45 man that scared the shit out of me
Haha
College Algebra ain't got nothing on me with the help of Logan lol.
you got this!
that kid scared the shit outta me
you saved me
I loove you
جميل
Brian wish me luck tomorrow
you got this!
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.
That’s what I was thinking ! I was looking threw the comments to see if anyone else thought so as well
That's what I was thinking tooo!!
What grade is this
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….
you have to include the 2x^2 too. use "magic x" method facting out the (2x^2 -x -6)
I know this is an old video but damn this is why I never understood math. Like how do you know 6x is x-1 is it because if you have to always divide it by itself when its with a letter? Or is it because it's written like a fraction? And that just leads me to ask of thats the case why doesn't the same apply to questions like (2x+1)(×+3) or does it?? I'm 28 and tried my best to understand mathmatics and no one was ever able to explain shit to me. I literally remember every damn teacher saying "well that's just because that's how it works" BUT THEY NEVER EXPLAINED
All that work for 1 answer these are tedious more than hard for me
Great instruction, but unfortunately I think some of your students haven't learned how to multiply yet...
haha probably true
Good teacher, just sad he has the worst students lol. High schoolers smh😂
12!