Algebra - Simplifying Complex Fractions

This algebra video tutorial explains how to simplify complex fractions especially those with variables and exponents - positive and negative exponents. This video contains plenty of examples and practice problems for you to work on.

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/

[@bei2426]

in one of the most top comments on this video someone states that 2:19 has a mistake and the answer should be 9x/4y is this correct?

[@Illuminous_]

2:10 a little error flipping the second fraction there

[@TheWayEverlasting]

@Illuminous_ yes he made that error when he flipped the 32 over 48, he turned it into 48 over 24. This shit had me bugging out because I knew my math was solid, so I went back and reviewed it. Dude is still a pretty solid tutor but man this had me trippin

[@TheWayEverlasting]

@TheOrganicChemistryTutor You flipped equation wrong @2:18 and put 48 over 24 instead of 48 over 32. You got folks bugging out trying this at home 😅

[@alexcordero6672]

I watch these and say, "ok, that's easy..." Then I look at my actual problem and it's like starting from scratch... Every time. I don't know why this doesn't stick

[@slowryd3g]

You are concentrating too hard. Take your time and relax.

[@AlexandrBorschchev]

Instead of watching, try the problem to yourself. Thats what i do, avoid watching and going ‘hmmm yes thats how i would do it’, instead try doing it yourself in paper.

[@nilen]

@Asher and Brianna yea you need to actually practice not just watch it..

[@alecthomas7408]

IQ isn’t high enough.

[@Shadow_1222]

@@alecthomas7408 while high IQ might help in Math, most of the time it's Memory and Reading Comprehension that would help you pass Math.

[@joellebryceroque4698]

In 2:19, the denominator in the other fraction should've been 32y. Hence, the answer (3:26) should be 9x/4y.

[@successekwe3661]

Yeah

[@fezani5149]

yooooo I thought i was going crazy lol

[@ethanlewis1536]

Thank you because I was like wait what, why is my answer different

[@loveinterest8714]

@@fezani5149 BYEE BC I LITERALLY RE DID IT 4 TIMES

[@blueteardrop5783]

Omg I thought I had to restart the full thing again thanks so much😭😭😭

[@toms.6685]

You messes up the second problem is was 32y not 24y

[@selenawang5200]

should update the video

[@laurenstewart5707]

Tom S. &

[@filipborin555]

Yup fella good catch

[@larainelaraine]

Yes that is why my real answer was wrong my real answer was 9x/4y

[@sterlingkingdoesit]

Althea Patience was this the right answer

[@achadavid2302]

13:34 not sure since im self studying this... but 4y should be there since 4 is cancled. So its supposed to be (5+y)(xy)?

[@F11.]

yup!

[@chadeonjohnson6837]

King Chocolates exactly

[@manlikezakaado6135]

Yeah maybe he forgot, but he is really good teacher

[@saki7952]

Yes, you are correct.

[@lastchance8142]

I knew it! He should do these problems before he presents them. Now, what is the correct answer?..I got (xy)(4x-5+y)/4(3y-8x)

[@monkstiny.1070]

Me watches a math vid Ad : *ARE THE VIDEOS FROM 2006 REALLY HELPING??*

[@qsapolo1449]

Yes

[@Modgey]

*YES, BECAUSE NUMBERS DON'T CHANGE YOU LITTLE SHIT*

[@spacecowboy2160]

MonkStin Y. Actually yes 😂

[@sherpalakpa2]

@@Modgey I don't usually read comments but here i am lol

[@joseantonioperez5989]

Lol

[@Hannah-kt2tk]

2:16 you confused me cause I thought that the actual given was 24y but I replayed it and got even more confused as I saw 32y haha

[@jiee3123]

ya its 32y why it become 24y

[@Saint.questions]

im here for this too... it was changed i think he had a brain fart....

[@thebosswow4630]

@@jiee3123 hhhhhbme to i gat mad

[@nackyding]

at 2:23 how does the fraction 32y/48 to 48/24y? Shouldn’t the reciprocal be 48/32y?

[@rexd1624]

typo

[@kamilaperez9781]

He wrote it wrong by accident

[@veestu9308]

The real answer is 9x/4y

[@hexagonmagnetics569]

9x/4y is the answer

[@sanopann1896]

@@hexagonmagnetics569 can we still reduce 9x/4y?

[@DevAngelo]

You should add a popup explaining your error on the 2nd problem so people don't waste time trying to figure out what's wrong.

[@chainsaw2046]

Yeah, thanks for the comment, I was like 'wait wtf happened to the 32, it Def doesn't simplify into 8*3'

[@mrilovegod370]

are the videos from 200blabla really helping....lmfao yes they are.

[@highthoughts6984]

LMAO 😁

[@filipborin555]

Yup cuz the math is the same it isn't a new ford model :D

[@nicholasr5146]

Math doesn’t really change lol, why would it?

[@Increase_the_dose]

Lol. Like when was the last major revision in Algebra? Wayyyyyy before 2006. Love these videos. Although this one has two errors in it. Ayy.

[@MaddeMay33]

I thought the same thing, "StudyPug"!

[@hash8162]

Man you're the only reason Im passing my college algebra class. Nobody else makes sense to me.

[@rashidibrahim979]

at 13:08 i think its xy not 4y

[@mryup6100]

Yep

[@franklinokeke8369]

I saw the error too.

[@joshualamb2742]

agreed

[@serogolemogole2685]

Yea, but it's an honest mistake really, what matters to me is that he explained everything so well

[@ryanpagayunan2433]

Yep

[@savvystylelady]

Many many thanks to you! By Joe, I think I’ve got it! Your technique for solving these complex fractions mesh really well with my brain. I’m so grateful!

[@jamesmullen8147]

British

[@uwubermensch]

You're my favorite math teacher on youtube, you explain things in a way that makes sense to so many people. I can't thank you enough for the progress I've made. With that being said, I see you've made a few mistakes in this video, you are human, it happens. But I would hate for someone to not learn this particular "math skill" or get discouraged due to the mistakes in this video. I would highly suggest a redo of this video so that people can better understand what you're trying to help out with. Thanks again for all that you do with your channel, keep it up, you're helping countless students.

[@eltururuu1494]

It's the music in the back ground. Lol

[@nena_nezali]

Thank you. I was struggling with the khan academy course on nested fractions, and your explanation made much more sense to me.

[@skywatcher651]

3:40 - answer should be 9x/4y

[@sudaisshah9393]

how did you get that?

[@munchycookie9455]

Thank you! Taught me more in 1 minute 52 seconds than my math book did in an hour. New subscriber!!

[@lauragreer9444]

the vid was 20 min

[@cosmiceggs2385]

13:06 If the 4 is cancelling, isn't it 5+y times xy? Why is it 4y?

[@snwsurfbrdr85]

Video was amazing and just the right pace for me.

[@Kalliegurl]

Thanks for the breakdown it was helpful. There were a couple of human errors but nothing you didn't already tech me how to get around 😉

[@annikacalibjo9615]

Thank you for helping me understand the lesson! The book did not explain well, but you did.

[@bumbum7459]

True happiness is when you finally understand a math lesson 😭 I truly appreciate this video!

[@chrisatanasov8478]

it took 35 seconds for you to explain what to do. Its midnight and I'm writing tmrw but with you ill be fine. i love you

[@mnynlvr4347]

in 12:57 shouldn't it be (5+y)(xy) since the 4 from 4xy cancels out from the denominator? i'm not sure i followed why he multiplied 4y instead of xy

[@armanomadto58]

True

[@louiseangela3980]

How is xy the common denominator of xy and y???

[@vaibhavdadas5372]

at 6:52 by cross multiplying you will find 3x + 2y / xy sooo xy is common

[@ethanlewis1536]

I’ve found a couple errors. One of them I’m sure you’re well aware of between 2:19 and 3:26, where you made 24 the denom instead of 32. At around 14:00, you wrote 4x^2y-(4y)(5+y), the (4y), should’ve been a 4x. Overall really informative videos, but you have to catch these errors, it can cause a lot of confusion for watchers who don’t catch these.

[@RenGoneMad]

Thank you so much! I kept staring at it wondering where the X went and not being able to figure it out. I'm glad I'm not quite as stupid as I was fearing for a moment there. ^_^" Thanks for the correction!

[@taulguedi637]

I REALLY like this man... but I was having a hard time here. Thank you for the comment.

[@beroayman6934]

Actually the (4y) should’ve been a (xy)😀

[@joymee5337]

@@beroayman6934 Thank God I saw this! I was wondering whats wrong with my solutions

[@abdullahtahaam]

true that, i was wondering why my answers are not coming right

[@haekim3058]

Your videos help so much.thanks to you!

[@chamas3331]

you made several errors during this video just check the comments, you should update this video and im not saying to be a douch i just think it would be a lot more helpful with the errors being corrected. thanks for even making these videos in the first place though seriously

[@kristianchoate5869]

Your voice is so soothing. Thank you

[@maliyahwilliams3281]

This was so helpful... thank you!! 💛

[@cmejia4401]

I really like this channel thank you very much

[@alexawesome2194]

You really helped me its like you saved me

[@particleonazock2246]

Hey, Organic Chemistry Tutor, regarding the last problem, what if you have three variables? How would you simplify dat?

[@bakedeggplant7203]

At 2:18 instead of the second fractions' reciprocal resulting in a denominator of 32 you put 24. It's 32 in the problem.

[@kaashvisingh17139]

Exactly!

[@emanuelramirez2570]

@@kaashvisingh17139 I thought the same thing, something is not getting well. At least I understood how to solve problems like this!!!

[@osapreaches8949]

Me too i got thought the same thing

[@blairLK]

and then he cancelled out so theres 2y at the bottom but he thought it was 24.......

[@candygirlygamer1640]

Yeah it was suppose to be 32 not 24 but it's grand now at least we know how to do it

[@Grimthunder338]

at 13:07, why would it be (5+y)(4y) when you already cancelled the 4 out when factoring for the other half of the numerator? wouldn't it just be 5xy^2?

[@jerihallberg5875]

baby steps, quiet atmosphere, my favorite beverage, lots of paper... very relaxing!!!

[@tubeblack35]

Yes this stuff is cool.

[@skywatcher651]

14:40 Shouldnt that be (4x^2y-5xy+xy^2)/(12y-8x)? And xy(4x-5+y)/4(3y-2x) as the final factored answer?

[@tubeblack35]

I got 4x^2y - 5xy - xy^2 all divided by (12y - 8x). Did it two different ways; same answer on both.

[@alexanderoday6411]

that's what I got

[@jeremykeddie4605]

xy(4x-5-y)/4(3y-2x) ... the y variable in the numerator should be negative since it's - (5+y)/4

[@blastoff2022]

you really helped me! Thank you!

[@HAWK45454545]

It's confusing when you go to find the GCF... I get really confused on why you pick certain GCFs and I think I'm going to fail my test because of it.

[@hiam1709]

Thank you so much! Ur videos are very helpful I have an exam in a day and i still didn’t understand those and not mention I got 6 lessons and I only understand till now 2 of the 6 lessons! Thank you soo muchh!

[@ravishkasilva2851]

Thanks for these lessons

[@fat70girl]

Outstanding review. Thanks for the post. It is a bit much to take in. Much of your detail is new material for me, not seen in high school. Is there a procedure to obtain permission to use your material in a the classroom?

[@TheCbrown146]

I think you can tell the kids to look up his channel. My professors tell me to look up Khan academy all the time.

[@owenreel3916]

legally, as long as you are not selling his videos and downloading them, you are allowed to show whoever this. You just cant make a profit from it. Posting anything to KZbin immediately gives consent for anyone to share the video to anyone if available, and this is very much so.

[@mrjn6940]

hi mr chemist. can i use factoring method system for simplification method?

[@brylerevelar6755]

Hey Mate! You messed up the 2nd example it should be 32 not 24. So the answer maybe 9x/4y?

[@DaelinTV]

If our common denominator is 4xy @12:55, and we factoring that into 5+y/4, then the 4's cancel leaving us with 5xy + x(y^2). But yet he says the 4's cancel and instead cancels the x. This is a mistake right?

[@armanomadto58]

True

[@user-mx7qy2jx5w]

Your content is awesome. Your tutorials are even better than my teacher's teaching methods. I understand you much better than my teacher 😂 thanks a million 😅 😊

[@inthava]

In my country if you want to do math you have to know English and learn with this guy. Thank you a lot ❣️❣️❣️

[@programmerbd1486]

Where are you from?

[@inthava]

@@programmerbd1486 LAO P.D.R

[@jaam950]

Thanks man you help a lot

[@harvymontales1820]

bro this man made math with letters easier.

[@janaebandy1070]

Ok why did my math teacher make this harder than it actually is ?

[@slowryd3g]

I have been saying the Same thing! Give it to me in plain english So I can work with it. Then give me the technical terms.

[@nihilisticemoidiot5813]

My maths teacher shows us even better short cuts than him, though the teacher is new, before hand I used organic chemistry tutor because the maths teacher did complicate it a lot.

[@varsha_raj]

Thank you so much sir 🙏🏻

[@kingicecream8585]

at 8:18 when you are "factoring out an x at the bottom" What does that even mean? How does the answer change so much? I have no idea what is happening there

[@laurenceniniel8160]

You notice that there's two different answers the 5xy-x and x(5y-1) right? Now go try distributing "x" from the answer x(5y-1) and it will come out the same answer from the first answer. In short, x(5y-1) = 5xy-x

[@GabrielTobing]

I keep doubting myself and so I confuse myself every time, thanks for the video.

[@robox8806]

Thx mate you helped me a lot

[@kianchua8581]

thank you very much you teach better than my actual teacher in school

[@donmarz7030]

Thank you sir for posting this video. But i sir i wan to know what happend here at 12:54 to 13:09 you said the four cancels, then there is this (4y) or is it maybe (xy)? I got confused on that on that one sir.😔

[@blairLK]

its supposed to be (xy) yea he got confused

[@anapacheco4320]

How would you simplify an expression like this: (6/(6/x)-3))+3 My problem is that I don’t know what to do with the +3. Does it still get multiplied by x??

[@sajeshsridhaarshan641]

thank you. I understood now.

[@kennethbachstein8202]

Thank you! I was picking my brain for a while! This really helped.

[@user-cr9zc9ih4q]

Why is the 32 become 24???

[@criticalsage9834]

u called reciprocal a "FLIP"??

[@Nourhan7777]

Yes

[@c_rem6101]

They grade you on your work not your vocabulary 😂

[@ttvandibro_yt5647]

you flip the second fraction so yes

[@azamalimari4952]

There is a fraction where you made some changes in denominator for 32 into 24

[@sk8n854]

Best math videos on the web. Bar none.

[@MikeOtranto]

I love your channel. Especially when you reveal that you're from NYC by saying "fow-tee" instead of "forty." I moved away in 2005 but I still let my accent slip every now and again.

[@IceyDivine]

I swear I love you xD you break everything down to nothing

[@blueday4644]

Agree, simplification of unnecessary complication to problems within the 'standard' math textbook.

[@BradleyMcDonald-jf6bj]

7:39 so why is the common denominator xy and not just y if only y is in both sides of the problem?

[@laurenceniniel8160]

It's because "xy" is the most dominant denominator so that's why he used as the common denominator which is still valid since there's still a common "y" on both sides.

[@isaac95395]

7:57 how come on the numerator the xy's dont cancel all together leaving just 3-4 ?

[@chazmichael7967]

l believe only denominators cancel out?

[@laurenceniniel8160]

@@chazmichael7967 yes you're right, you can only apply the cancellation on numerator-to-denominator or the other way around

[@zarawoods6973]

Why would the x cancel out if you are multiplying not dividing 13:36?

[@zacharynazareno2294]

Ty very very much this really help me

[@ryantay867]

Nice video. Thank you

[@user-qh6vv6hi5g]

Was the 32y written as 24y by mistake at 2:16? Love the rest of the video. Thanks.

[@hussanara9592]

Thanks man appreciate it G

[@issasaadiq794]

Shouldn’t one over y times xy be 1x instead of just negative x, cus what happens to the 1?🤔😕🤷🏾‍♂️

[@pillowyflunky9931]

Thank you so much

[@mlgaming7308]

what app do you use to do that

[@xTriplexS]

2:18 if people are confused why he wrote 24Y, it was probably a mistake as the flipped version should have been 48 over 32Y and I believe the result would have been 9X over 4Y

[@j1mer393]

how do you do this??? You just make everything you say make sense. Cant seem to figure out why my math teacher doesn't.

[@keilansnider2157]

What if there is no common denominator between any the fractions in the equation?

[@celineeng9167]

Can someone pls solve the problem at 12:38?He did 1step wrongly(should be xy not 4y) and now im stuck

[@JustinJackson-hp1wt]

thx u. i thought i was wrong lol

[@nararabbit1]

I got 4x^2y - 5xy - xy^2 on top, factor out xy for xy(4x-5-y)/4(3y-2x).

[@stranyl]

Thankyou so much!

[@bunkingwithharleyonaverylo2936]

Thank you sooooooo much

[@marilynfourie5408]

13:09 if the 4 cancel and we are left with xy how did he multiply by 4y?

[@akariovo7505]

My math teacher is making us do these but we also have to factor them at the same time which really hurts my brain. Sometimes when someone is confused he accuses them of not paying attention in class so its been really rough.

[@idisxgic7651]

Where did u get the first 24 from when u said flip it it would be 32

[@googleuser630]

3:26 The right answer is: 9x over 4y

[@Omkar3324]

Thank u even I got confused

[@pooodonklooopdoop5672]

Iv’e been here so confused for like a solid 20 minutes.

[@heyfrosty9429]

This guy is better than my math professor

[@nathanmoya2769]

7:38 But why is xy the common demoniator if y appears two times?

[@jerichoguillermo8699]

In 19:15 why did you not cancel both x-1 and x+2?

[@JuliaLaur]

Answers that I got for #2 and #9 2. 9x/4y 9. xy(4x-5+y)/4(3y-2x)

[@jadenstock]

Life saver!

[@bookert.w2022]

Why in 16:31 is x^2 the common denominator?

[@tori-sg2pi]

at 16:26 why don't we multiply the fraction by (x)*(x^2) why are we able to only multiply by x^2

[@markandrewbautista5539]

THANK YOU

[@caspermoes6762]

Love the vid :) A minut mistake at 13:00 where the laster factor in the numerator is supposed to be (xy) not (4x)

[@gervinpaguntalan9434]

what if it is F your variable at the dinaminator

[@Bleepblop223]

At 13:13 I’m confused at why it simplifies to (5+y)(4y) where does the x go? Wouldnt the 4s cancel out and then it becomes (5+y)(xy)??

[@user-xe7dx8un3i]

he made a mistake, you're right!! correct answer is: xy(4x-5-y)/4(3y-2x) when factored at end

[@janevite6965]

D@mn, 4years ago??? Its still helping after 4yrs

[@annego3656]

Thank you

[@xiameaesmabe1386]

Waittttt isn't 8•2 equal to 24? But the second problem had 32 on the denominator of the second fraction >:0

[@willowfield5100]

Xiamea Esmabe I realized it too. So what actually is the correct answer?

[@saniyarajput6149]

Correct answer is 9x/4y

[@tokyorio6710]

very helpful (y)