Algebra 2 - Solving Rational Equations
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- Опубликовано: 6 сен 2024
- Solving Rational Equations means knowing how to manipulate fraction (rational) expressions that include variables, in order to solve. We use common denominators, which is your favorite method, OBVI. That means obviously, OBVI. YAY MATH!
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This guy just seems so passionate about this job, he really seems to /want/ the students to understand what is going on by making things simple. Props to you man.
I wish I had him for a teacher. Life would be so much easier
ikr
Qetsia Etienne same. This guy is a great teacher.
You're so kind. The good news is that I kinda am.
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wow you really are a good teacher DONT EVER STOP PLEASE I dont even understand what my teacher is saying half of the time. YAY MATH
For some reason my bizzare boy math teacher sucks at teacher so now I'm here at 12 am before a test
same lol
I feel it.
bruh I'm here 2 hours before my final exam
When solving an equation like 3·x/(x - 5) = 5 - 5/(x - 5), I would recommend to not multiply by the least common multiple like it is being taught. The problem with this is that it often introduces extraneous solutions to the equation, and it can make the solving process more difficult, by making you solve polynomials with a degree higher than the number of solutions.
I would recommend (1) bringing every fraction to the same side of the equation, so 3·x/(x - 5) = 5 - 5/(x - 5) 5 - 5/(x - 5) - 3·x/(x - 5) = 0. (2) combine all the fractions into a single fraction, which can be done when the fractions have a common denominator. You can achieve this is if you rewrite 5 as 5·(x - 5)/(x - 5), or as (5·x - 25)/(x - 5). So a student can write (5·x - 25 - 5 - 3·x)/(x - 5) = 0, which can be simplified to (2·x - 30)/(x - 5) = 0, or even 2·(x - 15)/(x - 5) = 0. (3) divide out the common factors. In this particular exercise, there are no common factors other than 1, but in other exercises, this step would be necessary. (4) multiply by the denominator on both sides of the equation. This gives 2·(x - 15) = 0, which is easy to solve.
This method works for all rational equations, has the same amount of steps as the standard method, sometimes less, and it avoids introducing extraneous solutions. For example, when solving x/(x + 2) = 6/(x + 5), you can write x/(x + 2) - 6/(x + 5) = 0, and combine fractions by writing x/(x + 2) - 6/(x + 5) = [x·(x + 5) - 6·(x + 2)]/[(x + 5)·(x + 2)] = (x^2 - x - 12)/[(x + 5)·(x + 2)]. So you get to write (x^2 - x - 12)/[(x + 5)·(x + 2)] = 0, which is just a single fraction. Next, you want to factor and divide out the common factors. x^2 - x - 12 = (x + 3)·(x - 4), so (x + 3)·(x - 4)/[(x + 5)·(x + 2)] = 0. Since there are no common factors, it is now that you can actually multiply by the denominator, and simply obtain (x + 3)·(x - 4) = 0. This guarantees that neither of these is extraneous.
Can you make a video? I would watch it.
7:21 15 minus 5 is not 3... if you plug in 15 for x, it will work out but he messed up there
Your the only reason I am passing my Trig class. I love you. God bless.
SO great! I love the way he takes everything step by step all while being entertaining!
I wish I had a teacher like you man!
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Keep doing what your doing man awesome work it makes so much sense to me
I am struggling horribly with Algebra 2 right now, this really helped and I love your teaching style! It's so engaging and super refreshing compared to my teacher. THANK YOU YAYMATH!!!!
I learned this in a book called Practical Algebra: A Wiley Self Teaching guide. It was in a chapter called fractions. In that same chapter, I learned how to divide polynomials. I didn't think I was as far into Algebra II as I am.
The only things that the Wiley guide didn't cover were Logarithms, Matrices, and many of the foundations for trig. I obviously needed to go back. I would like to get to a point where I take calculus in my first year of college.
Spectacular teacher! What a gift to the world! Thank you very much, and YAY MATH!
the teacher that i ever got in life is mean hateful this one is da best
Thank you now I'm not gonna drink bleach
I wish my teacher was like him 😩 she only gets mad when we don’t understand and hates repeating herself when we ask for her to repeat b/c we didn’t understand 😏
Thank you so much for helping me!!!!!! I had so much trouble with this and i have a test on the 2nd and now I finally get it!!!!!!
"I will see you in the afterlife"
This just in! Math teacher brutally murders a class of students
not funny dude. need to work on comedy. your not jimmy kimmel :d
@@ttvurmom6185 Lol. It wasn't funny until you said it wasn't funny. You even brought up Jimmy Kimmel, which made it so funny that I literally peed myself in public laughing.
How would you treat the first coefficient 1, in this equation, and would 2x(4) be the common denominator to use? 1 - 3/2x = 7/4
Thank you for doing these videos. These are helpful. I watch them because you're entertaining and it helps me pay attention better. Thank you!
Could you please work out 1/2+ 2/2x
Thank you so much for making this! I watched many videos and this one jogged my memory and I was able to help my daughter! Thank you!
This is in my Algebra I class and this lesson helped me a lot thanks.
Bless this man. I like math, but my current math teacher is making me resent it haha. Thanks YayMath!
Thank you so much! I have seen the majority of your videos and I love them, they have helped me out a lot in my Algebra 2 class!
4 years later still saving lives with the same video.
You are a lifesaver! The class is great too, because they ask the questions I'm thinking :)
Everyone think about maths teacher 😱😵
After looking at him : I wish he should be our maths teacher
How do you solve this problem , i am really confused (4a^3b /a^2 b^3) ( 3b^2 /2a^2 b^4) . I wish your my teacher, YOUR AWSOME .
good job you're a great teacher
I don't know how you can do what you did to solve 3x+5=2x but when I solved it, I had 5 instead of -5. I googled it and it said 5 was the correct answer. So....Please tell me what is correct and what is incorrect because I have to study for a test.
subtract 2x from the 3x on the left side, so now you are left with x+5=0 now you need to subtract 5 to both sides, so you have x=-5
the second example I got the answer x = 25/2
if I put the 15 inside it will not get the answer 5?!
What is 6/x-9/x-1=1/4 ?
Can someone please explain why he wrote down 3/5 @ 7:25
Is it even relevant to the problem or it is just there just to be there?
He is subtracting 3x-5x not 3/5
Thanks broham this vid helped out a lot
On that last example wouldn't it have been shorter to cross multiply?
FireWolf7 you have your way, we only have time to do it this way, DO IT AT HOME ajjajaja
hey man what happend to 3.5 & 35 and why did you put it as 6
how did you access the quizzes?
YOUR MY DREAM TEACHER XD !!!!!!
+James Silverio Youre**** your subject needs to be english not math
+SourHD You're**
+clawedhunter005 ure
but arent you supossed to multiply the x-5 times the numerator too?help im confused
The point was to get no fractions so it would be easier (:
Captain, you are fantastic!
Man He had so much fun for teaching that damn algebra ;)so does the students.
Why is x2
-12
Equal to x2?
Now I'm listening to that song in the background! Thaaaaannnnks. lol!
Thank you!!
Thanks this is helping me with my solving rational equations hw
Wishing my teach is like this, .
Can't you cross multiply the two fractions ?
no because this is an equation. you could do that if the equal sign was a divide sign.
He did, essentially.
You are my savior
What do you mean by 6 cancels with 6
6 divided by 6 =1
Thanks sir, it was really helpful
thank you! it helped a lot!
Yay Math!
OK so in the beginning (0:49) you say what is the GCF for the equation, but my math teacher says we need to find the LCM for these types of equations..What difference is there for these, and which one would be easier to use?
same thing
Good catch!
Not the same. LCM is used for these problems. LCM of 3 and 9x would be 9x.
He corrected the student and immediately made the same mistake.
GCF is used to simplify.
yo this guy is amazing!
Is this Algebra 2 or Algebra 1?
i wish I have a teacher like dat
can you teach at my school please lol
my math teacher doesn't teach and is so boring and does the exact same thing everyday. just different math
I didn’t understand where is 3x?
7:21 is 4.5=4.5
6x-6x is twelve??how??
It’s a not a greatest common factor it’s a least common multiple
-Kashish
Yay Math! :D
what school does this guy teach at?
+afg229 yay school
+afg229 he said he lives in Malibu, which is in LA, so its a school in California
David Coupel yeah i found out where he teaches
+David Coupel that explains why the kids are so annoying… they're from California
Reagan D shitty logic
I use these videos for my math classes.
no one, no one, no oooooone.... XD
Guys! X^2 + # CANT be factored. X^2 - # CAN be factored! This fucked me up on a test and I failed it.
Adam sandler as a math teacher
0:48
he should have said LCM not GCF
Not all of rational equations are being taught but I know all of it from my textbook. It's more complicated than what he taught like he forgot to teach the x cannot be part because that matters as well
I'm don't understand any of this...
at 7:03 where did he find that -5x???!! PLEASE ANSWER ME BECAUSE IM GOING TO REPORT THIS IM CRYING
from the last fraction -5 is the only thing that is left
IM UR BWI there is no hope for you I'm sorry
too bad my math tests are way harder than this :|
3 does not go into 16 evenly. Sorry simsek cool
Opmathera? XD I'm a comment junkie...
I will comment on anything funny in the videos I see.
WTF is this and cen someone tell me how to do this? y=5x-9/3x+4
for x
kkkk
ow omg 666 that number
Oh my God thank you!!! I was about to shoot myself
IM 12, WTF
You should stop saying over nothing/multiply by nothing. When you clear the denominator, it's still over one, not nothing. When you don't multiply because the denominator is already the lowest common denominator, you multiply by 1, not nothing.
Kiss my ass
Oh my God thank you!!! I was about to shoot myself