99% of Algebra Students don’t UNDERSTAND this…. 

Many words. Just directly discuss on the computation as simple as possible.

If 99% of Algebra Students don't UNDERSTAND this, then they have had very poor tutelage.

Problem solving starts at 7:00!

Thank you.....Just purchased your math course for TEAS.....Thank you for giving all of this information

To much advertising; to little teaching.

Boet...you are great and don't need to tell us for the first minutes what you offer...just solve the equation and teach us.

well, you can set D=0 , determine 1 cannot be x. And, later you can divide out (x+1) just leaving 3(x-1)=5, x=2/3. Plug inn x to verify and call it a day.

Thank you for sharing your knowledge,

This confused me a bit, since it's counter to how I was taught. You see, *before* solving any equation, you have to discuss legal values. For instance, if you are asked to solve [x^2 + sqrt(x - 1) = 4], then what is really meant is find the set { x | x^2 + sqrt(x - 1) = 4}. Implicit in the notation is that you can't take square roots of negative numbers, so you need to assume that x - 1 >= 0, or x >= 1. So, to be more exact, we need to find the set { x | x >= 1 and x^2 + sqrt(x - 1) = 4}. In this case, implicit in the equation is that the denominator can't be 0, which from the get-go precludes x in { -1, 1}. That should be step number 1, and not part of the "check" at the end! "Extraneous" solutions are a misnomer. Every time you multiply or divide LHS and RHS, you must add another condition. If I multiply (x-1), then I must assume that x is not 1, because otherwise, I multiply by 0 on both sides, doing the useless work of proving that 0 = 0. If I later get a "solution" that x = 1, it can be immediately discarded because we assumed that x could not be 1! Anyway, the real problem here is not understanding pre-conditions and not using logic reasoning and set theory.

Isn't it allowed to do a lim calculation? As a simple example, calculate f(x)=x/x for x=0. According to your explanation, this cannot be calculated. However, lim x/x for x nears 0, the result is valid and equals 1.

Do you sell your notes on hard copy? If not, then are the digital ones able to be downloaded and printed once purchased? It's just I work better with pen and paper. Many thanks.

To much off track talking " which ramp do I get off on". Get to the explanation quickly"

Great video. Thanks

Has anyone plugged the 2/3 answer into the original equation and made it work?

Thanks for your service.

where do you use that equation?

He still doesn't know the difference between a least common divisor and a least common multiplier.

I don’t remember learning this in high school. Would this content be in an algebra 2 curriculum?

Good, this hammered home that I must first seek the LCD. At first I did the prob by factoring but I sort of ran out of road. Why isn't zero a legit answer? Why can't I divide both sides of the original equation by zero and get, 3 + = ?

We’re not all cut out to be rocket scientist. Too much effort is put into teaching this stuff to those that will never have a need for it. But yes for those that are it must be available.

Please I love your teachings but the writings on the screen doesn't allow to see clearly I'd love if we eliminate the writings and keep the working screen thanks

Here is the straightforward method. 1) get rid of the fraction. One term is divided by x²-1 another is x-1. Which you should know is a factor of x²-1. So multiply the whole equation by x²-1 to give 3(x²-1) +10= 5(x²-1)/(x-1)=5(x+1) 2) expand 3x² -3 +10= 5x+5 3) collect terms 3x²-5x+2=0 4) solve quadratic. 4a) by factorisation You may be able to spot x=1 is a solution . So that gives one factors. (3x-2)(x-1)=0 x=1 or x=2/3 OR 4b) quadratic formula x= (5+-sqrt(25-24))/(2×3) x=(5+-1)/6 x=1 or 2/3 Check by substitution Note use of LCM is uneccesary in this case and confusing in general. Just multiply through by the largest divisor and see what you are left with after cancellation.

Greetings. We will rewrite the expression as 3(X^2-1) + 10 = 5(X +1) after multiplying all terms of the expression by (X^2 -1) and also with the knowledge of knowing that (X^2 -1) = (X-1)(X +1). Now from the rewritten equation we have 3X^2 -5X + 2=0. Finally, we factor the expression to get (X-1)(3X -2)= 0, and the values of X =1, 2/3

I need help with teacher certification. Please

Hi where are you from, sir. I would just love to meet your teacher.

I did it this way knowing that (x+1)(x-1) = x^2 -1 multiply both sides by (x-1) 3(x-1) + 10/(x+1) = 5 add the fraction "the bottom multiply the 3(x-1)" (3(x^2-1)+10)/(x+1) = 5 multiply both sides by (x+1) 3(x^2-1) + 10 = 5(x+1) reduce the number 3x^2 - 3 +10 = 5x + 5 3x^2 + 7 = 5x + 5 x^2 = (5x+5-7)/3 x^2 = (5x-2)/3 x^2 = 5x/3 - 2/3 2/3 = x + 2/3x - x^2 x = 2/3 or x = 1 can be the answer I guess since I don't know how to do the rest LOL

I guess I did it the hard way, once I got to the quadratic equation is used the formula: x = [-b ± √(b² - 4ac)] / (2a) and I got the correct answer using a=3, b=-5, c=2. It's been 40 years since high school!

Omg! I was thinking about getting a Mohawk!!1 mind you, it was because a librarian I work with has one , and it looks good so...another great little lesson btw!

very good review

You don't need to know about the LCD though. Just do what you do when you add somethin to a fraction. Multiply it by the bottom number and put the bottom number under it. Which is essentially multiply it by 1.

i was cringing the whole time during the intro. please get straight into the explanation and less advertising

I do understand this quite well, but honestly you teach it in a very confusing way. Just make the factors and steps bare simple and explicit rather than point with a cursor and hope the user pictures what the mouthful you’re saying looks like. Information hiding/reduction and being explicit with EVERY step is crucial. And, economy of words. Just put out a thought, pause, write, pause, next thought. That’s my advice if you want to reach people who are confused.

when I see x²-1 i see xx-1 not what you showed

Wait. 1 counts as a correct answer?

You should FIRST factor the denominators and list the POTWENTIAL extraneous roots.

I'm perplexed.... with golden rules of algebra one can rearrange the equation to no longer have those divide-by-zero denominators...

I see that you are talking more than necessary, try to take direct action to waste less time,thanks a bunch 🙏

I love "X" trainee us solutions !

this is good stuff, but you should have specified that x can't be equal to 1 or -1 in the first place. students shouldn't wait to check an answer to specify this, they should be in the habit of making it clear that any denominator can never be 0

I'm confused... Using algebra I can get those denominators REMOVED. Once removed the roots are ALL viable.

"I wasn't that good at math in highschool" Explains it all

You didn't know it either until you learnt

X = 2/3 Therefore 15 = 15

Very odd proces. 99% teacher don' t know what is shortcut method😂😅😆

Do you ever cover problems that actually cannot be solved in one's head?

I get X= 2/3 as the only possible solution.

I cant, for the life of me, see the value of knowing this information...

I would have shown how to solve it in less than 30 seconds!

Multiply with x^2-1 and set the right side to zero and solve Don't think that 99% don't unverstand this problem. It's to easy.

99% of English Students don’t UNDERSTAND the words 'go ahead' are usually completely superfluous

Are your notes giving the the real and true answer to the question and showing the real and true way of showing your work hint hint

You need to cut down the fluff off your video. Too much unnecessary wasteful tangents. The first order of business in a fraction is tgat you must not have a zero in the denominator. So x cannot be equal to 1 and cannot be -1. This should have been pointed out first. Then solve the other extraneous solutions. 5 minutes flat

Lot of comments over your stretch of videos with people saying talk to much etc.. this content is fantastic. Keep teaching.

Es fantástico a donde nos pueden llevar las matemáticas.

After sitting waiting for the product advertisement to end, you start talking about lowest common denominator. After going on about LCD for several minutes you say this video has nothing to do with LCD. We are now 1/3 through the video and nothing has been done to solve the problem. At this point in time I think I have better things to do.

Agonizing

Hate to be rude but there’s so much babbling plus this is hard to follow and understand compared to another video that was less than 3 minutes that was clear and clicked in the first minute.

If you make a discusion about a solution so unnecessary complicated I can imagine that 99% doesn't understand it. All that extra information is just confusing.

Sorry to say that your solution is fundamentally wrong! You should actually multiply all terms with (X^2-1)(X-1). This leads to a third degree equation that has up to 3 solutions! In your equation two out of three solutions coincide, so you did not notice the missing solution! When I make a minor change to your original equation: replace 10 in your equation by 9; then we find really three solutions, namely X=1; X=(5+/- SQRT(13))/6. Shall we say that the equation is too difficult for 99.9% of the students?

The point about extraneous roots is good but unfortunately, he gets it completely wrong at the end as 0 is a valid solution to both x^2 = 3x and x^2-3x = 0!

What don't 99% don't understand

Watch from 7 minutes to 17. The rest is a waste of time

First Time! You don't to multiplicate by x²-1 to the two menbres of the equation, you don't know, if this expresion is equal to zero, because when x²-1 is zero, you don't to multiplicate the two menbres of equation. Do you know, what is the first step when you start to resolve a equation? I see that you don't know. Is posible to multiplicate when you considerate what x²-1 is not zero, The next step you know, is posible to cancelate the same factor, on your exposition is not posible, you make a mistake, because you would be dividing by zero, this is incorrect in elementary mathematics.

Hello

I wish that i had a teacher like you back in my day.

I can’t believe one could stretch solving this trivial equation to 23 min …

put in x=0 and you get -7=-1 and I realy don't understand that. If you want to solve the equation just multiply by x^2-1 and solve the quadratic equation resulting from that. No need to blablabla.

Dude, this jumbled up mess is exactly why I don't understand Algebra...

This is so stupid, how can you say that 99% don't understand? It's an easy equation, you can solve it in less than 3 minutes.

Factoring is useless. Real world equations almost never factor.

Ok 99% dont understand because you were probably their teacher😂

RA, RA, I, RA RA RA MY...RA RA.....Get on with it man.

Too many words! Put your pencil where your mouth is.

👆👆👆👆

Get real, how many people really use algebra in their daily lives. These equations don’t mean a thing to peoples live unless you teach it. Everyone that uses mathematics in life use simple math including banks.

Your explanation are so long and confusing....

Too too wordy. What a jerk.

I didn’t watch the long ass video

The Socratic math app gave me the answer, and worked it out step-by-step in under 5 sec… just saying.

I wasted 14 min of my life watching this video….

You didn't show us how to do it, you're just talking to much

Get to the point man lol

I am so tired of the preamble in each of your videos. 4:30 until you start. Even then, you talk about your other videos. Too much nattering. This could be taught in 5 minutes. I'm unsubscribed!

One small critque on your videos direction; you keep interupting the flow of explination with unrelated content, and for me, and possibly others, it's distracting. When I try to rewind, to have you repeat a portion of the explination, I am again met with unrelated noise. I know this is an old video, and perhaps you've changed your flow, but watching this specific video makes me not want to watch any of your others. But I see in the comments many people love your videos, so this is just to point out one aspect that killed it for me.

Jesus, man, there's a lot of wasted time and words here. How about getting down to business in 10 minutes instead of a 23 minute video.

Please correct the headline. »99 % of US American ... students ...«.

You interrupt yourself a lot.

It is a lot of blablabla….you should go straight forward to the point….the video become very annoying

Sorry but you talk too much. I teach in a prison; trust me, if you produced an explanation like this in there you’d be completing the problem in A&E 🤣

You talk to much

You really should talk less.