Partial Fraction Decomposition - Example 4
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- Опубліковано 21 жов 2024
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( • A Complete Partial Fra... ) Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Partial Fraction Decomposition - Example 4. Partial Fraction Decomposition - Example 1. In this video, I do a partial fraction decomposition where the denominator factors as a product of LINEAR and QUADRATIC factors.
You explained this in 8mins what my calc BC teacher couldn't do in a whole class period. Thanks!
@Maxdwolf it had a mistake, so i deleted it; i will remake it and repost it soon
I assume it never got remade? :(
you're the only reason I'm getting thru calc 2 lol
LOVEmac432 saaaaaaaaaaaaaaaaaameeeeeeee
6 years later and you're still a boss
+TheBigDdub yea, the good thing about this stuff is that it never changes!
@@patrickjmt hiiiiii
@@patrickjmt just learning the partial fractionss
@@patrickjmt Even when the night changes!
13 years later he still is a boss
Patrick helped me through my Electrical Engineering major 6 years ago and now helping me again through my FE & PE examinations. Man you are amazing!
ha, wonderful! best of luck :)
I don't know how many times I have came back to this video over the past 3 years. Thank you!
It's like Patrick teaches us how to count from 1-10 by ones while our professors teach us to also count from 1-10 but skips numbers in between🤒🤒....thanks Patrick you're the man💯
This helped me a ton with my summer homework so far! This probably won't be the last one of your videos I watch :D
Never in my life have I subscribed to a youtube channel, but after you helped me out so much it was the least that I could do. Great videos
i was looking all over the internet for help for a problem I'm working on. Should've just came here. Thanks!
Thanks Patrick you are the best teacher ever!
wow. I read the text book full of 3 pages of notes and examples and would not understand. I then went to class for 110 minutes and I had a lecture about this. Yet you some how explained it in a much simpler way. thanks I love the math videos in youtube. They are clear and straight to the point
hey,getting ready to go back to school, wanted a refresher, this has been a huge help.
simply you are the king of math
I prefer your videos to Khanacademy's videos. I think your videos get straight to the point instead of dawdling away time like some of Khan's videos. You also seem to cover topics he doesn't, which is a major help. It's a shame that we pay so much for education to teach us and we don't understand it, then turn to free resources to help us learn it. Thanks so much though PatrickJMT! I can only imagine how much your videos will help me in university in September.
Now why doesn't my textbook contain these simple steps to actually explain how we can do partial fractions, but instead uses confusing shortcuts to solve the problem...I think most of the time ,students do badly on math only because most of their textbook sucks
Nero Archon that is true T~T
This is so true, these videos are what we need. Step by step so we can understand why and what to do.
exactly
Better than doing badly on meth...
Lol, my book is exactly the same. It COMPLETELY steps over all the algebra to save page count. It doesn't even show a quick formula to get the desired result. I'm okay with some algebra skipping if it's obvious but this is a lot of skipped algebra that is basically the point of this entire technique..it's like showing how to differentiate while skipping the differentiation.
thanks! was having some issues with the repeated factor of x^2 and i've resolved it. i love all your vids, and you're gonna be the only way i get through calculus at my community college! (none of the professors can teach)
Once again saving college careers even 10 years later haha Thank you so much man!!!!
Thanks for posting all these videos up, you really are helping lots of people! you are better than my teacher in uni
You know how to explain things 1000% better than my teacher thank you sooooooo much all your videos related to this topic are great keep up the videos plz
YOU SIR HAVE TAUGHT ME 2 WEEKS WORTH OF CLASS IN 20 MINUTES..
I CAN NOT EXPRESS MY THANKS
This is the best explanation I've ever heard . Thank you so much now i can pass my calculus final tomorrow .
Did u pass buddy??
Did you pass buddy?
@@aarohansharma4551 I’m done with university and working . Thank you 🙏🏿
@@jidealabi5955 wow, good!
this saved my high school math test grade. Thank you so much!
wow! youre just the one who've explained that clearly to me. !! thanks patrickJMT
That was explained so simple, thank you very much.
I can't thank you enough thank you for this example!
Why shouldn't we put Bx over x^2 for the second term? Isn't x^2 a quadratic factor?
where is the example 3?
he removed it because of a mistake
I ate it sorry
@@ummeabdullah5347 it's ok. You must have been hungry
Thank you! You helped me with my math homework so much!
I swear I am going to be making a massive donation once i get out of school and into the workforce. You have saved my ass so many times its a little ridiculous.
this is blowing my mind and its been here for 10 years wow
Hi Patrick Sir , thank you for the video.
Thank you so much Patrick! you're a great help
im just a little confused when you start equating the coefficient and solving for A... if B=-1/5 you will get a different value for A depending on which equation you plug the -1/5 into. So how do you know which one is right?
I would be out of Engineering school if it wasnt for you. Thanks so much.
you have no idea how much this means to me right now
you're way better than my stupid calculus teacher in college. He doesn't explain this stuff thoroughly
Thanks for the video, great stuff. Where do you explain why a denominator of (x)^2 gets decomposed into x and x^2 rather than just x and x? I'd like to understand this properly.
THANK YOU I could not understand it when my professor was trying to explain but I get it now😥😥😥😥😥😀
Does the A, B, C value not have to be one degree less than the denominator?? Like instead of B should you not have Bx + C? I'm just wondering because in example 6 your second fraction was degree 2 and you put Bx+C/x^2+2x+6? Thank you in advance, these are really helpful videos
You're a top bloke Patrick!
How does x squared break down into x then x squared in the initial fraction set up?
So x^2 is quadratic. x^2 also equals x times x, which are two linear terms. You have to account for the linearity in the original addition as well. I know this is such a late answer but I hope it helps
@@ebbenflow_ Too late lol
Watching this with captions is informative and hilarious.
The degree of the numerator is it bigger or is it equal to the denominator? Because you have taught me that the degree of the numerator must be less than the degree of the numerator
I have a similar problem. A proper fraction with a linear numerator. The denominator is a product of a linear factor and a factor repeated 5 times, x^5. How do I approach this?
I am Chand Evil No worries. After finding 2 of the coefficients (A and F), I used 3 random values of x to solve for the 3 unknown coefficients using the system of equations (simultaneous equations)
@tiff4annie Nope, anytime you have an x power greater than 1, you need all the possible factors that make it up. For example, if you had x^5, you would need x, x^2, x^3, x^4, and x^5.
Another way to do this would be to use your trick of plugging in x values, and then just pick a value for x to solve for the last variable (since you already know what the values of B and C are). It's a little faster, I think.
calculation for non repeating zeros in 10 seconds: cover up x+3 in denominator and plug in x=-3 --> C=[2(-3)^2+4(-3)-5]/(-3)^2=1/9 done
when would you use ax+b in the numerator?
why did you put x and (x)^2 at the beginning?
+Harsh Patel According to his method, this allows us to have a visual cue that x^2 is a repeating linear expression rather than a quadratic expression that is repeated.
where is example 3???
he removed it because of a mistake
that guy is not exactly random
This was great.
what if the x^2 has a constant with it? for example (x^2+9)
Instead of making the denominator have 3 terms, I kept it as two (A/x^2) + (B/x+3). Would a solution to that be the same as using 3 terms (A,B, and C).
Hi Patrick..... your uploads are quite appreciated.thank u so much.
I got doubt that if we go by substitution method as
If x=0, we get B= -5/3
If x=-3 , we get c= 1/9
If x^2=0 , how to find 'A' value?
Please do explain?looking forward to your reply.
Thanku
you can use x=0 , x=-3 and x=1 for A by subbing in B and C and then just use basic lcm and then you just simplify the fraction and you get the same answer for A
I like you so much !!!!! really helping many students .thank you so much .i really appreciate it
thank you! but how did you know that you had to split up the x^2 into A/x and B/x^2 ??
On the power
cheers patrick you genius :)
very helpful Thank you
you are the only reason im passing ap math grade 8
happy i could help :) good luck in your class!
how can i answer a fraction form question example..
wsquared-1/2+3/16
Brilliant! Thank you!
Great Video !
You saved my ass way too many times. Thank you.
Thank you so much
One of my variables comes up a 0. A=0. is that possible? It'd cancel a whole fraction out. I've gone over my working and i haven't found any mistakes. :S
X divides into X^2 perfectly, so question is why do you have to put both X & X^2 as denominators on the right side..?
no idea, trash video honestly
Using matrices to solve for those constants is so much faster. id recommend it. but great video. Saved me a failing grade
thank you very much
I'm sure the equating coefficients is faster than the other method
aren't you supposed to include an x in the numerator that is one degree less than the x that is in the denominator? so if you have an x in the denominator you end up having Nx^0 which is equal to N and if you have x^2 in the denominator therefore you should have Nx
he explains what neither your textbook nor your prof doesn't
Thankyou....sir❤️❤️❤️❤️Thankyou so much🥰🥰🥰🥰🥰🙌🙌🙌🙌God bless you sir🌸🌸🌸🌸🤗🤗🥰🥰🥰🥰
When you get the answer, aren't you supposed to integrate it back?
I don't understand this. why does (x^2) turn into a/(x) + b/(x^2) ?
ok ;)
Can any one explain about how he just add an extra x at the denominator..
same here !!
why he added an extra x ?
because that's how it works bro, if u got a factor with a power more than 1, u gotta put the term without power first then repeat the term again until u reach its power. for example u got (x+3)^3, your denominator would be (x+3), (x+3)^2, (x+3)^3. there you go, hope this helps
thanx a lot.....
@@John-yahya do you still need an answer?
Isn't x^2 ia quardatic ??
Thanks champ!
♥️ words can express.
All college Math Professors SHOULD BE FIRED!!!!!
The horrible and egotistic College Math professors should be fired. Not all of them. Most of my math courses I had great instructors, except when I took Differential Equations for the first time. HE LITERALLY SAID HE WILL FAIL ALL OF US AND HE WILL MAKE THE COURSE AS HARD AS POSSIBLE THAT ONLY 3 KIDS OR LESS WILL BE LEFT IN THE FINAL. He's never done a partial credit for the class. One mistake means you're zero. All your work in the problem will not be counted. I still despise him to this date. He must have been bullied in his younger years lmaooo. I took it for the second time with a different professor(which is so awesome by the way), and GOT A FUKEN A IN CLASS.
i commented this last semester but oh my god hahahahhahaha my calculus professor is literally useless. he like types math out in paragraph form and reads it out to us and is like "get it? cooooool" without explaining anything. i almost cried the first lecture because i couldn't even keep up with review from last semester.
so i started watching these before lectures and now i know what hes talking about and don't hold back tears every tuesday/thursday. when i get a job i owe u dude youre basically my calculus professor this semester and the reason my grades dont s u c k.
thx (sry for the novel im just passionate)
What your learning this uni? i thought we got taught this in year 9 or something
i think it is because some country have different pace on their education. Because I learned this on uni too btw.
GOD BLESS YOUR SOUL
thank you very much wa kabaxasatay
What happened to example 3?
Okay, I do NOT understand why you had/have to pull out the A/X as well as the B/x(squared) as factors!?
why are the denominators x and x^2, can't it just be x^2?
No
and hire Patrick!
Why did he write 3Ax and not Ax + 3A and then write the opposite for B, 3B + Bx instead of 3Bx.
I have a question, so my partial fraction decomp was -2/(x+1) -3/(x+1)^2 + 2/(x-1) and i got -2ln|x+1| +3/(x+1) +2ln|x-1| +C now the correct answer has the same answer but without the coefficients of -2,3,2. Did i do something wrong? The original equation was (x+3)/[(x+1)^2(x-1)] . Thanks to anybody who can help!
could someone please take a look at the following:
x^2 -19x + 15 all over (x-1)(x-2)^2 = A/(x-1) + B/(x-2) + C/(x-2)^2 ... now it makes perfect sense to me that C/(x-2) is incorrect. However, (x-2)^2 = x^2 -4x + 4 and if you said A/(x-1) + (Bx+C)/(x^2 -4x + 4), you'd still end up getting the wrong answer. I don't see where the process becomes inconsistent.
Thanks!!!
at 6:58 why is it +5/3 and not -5/3 for B when you plug into 4= 3A + B
edit NVM: IM BRAIN DEAD.
really helpfull man
thank u very much
bless ur soul!!
my mind is blown
thank you very muah you the problem that bother me for fee months...
your my hero
thank u soooooooooooooo much..