x/4 + 8/x = 3 This Algebra Equation is NOT so simple! 

Keep the videos to 5 minutes maximum. I like learning but 16-18 minutes bores me so I have stopped watching/learning.

I eliminated the denominators and went straight to the quadratic formula, all in my head and it took max 20 seconds...

I'm using my RU-vid Premium subscription to learn freestyle swimming, math, Hungarian, Greek, Mandarin Chinese, and other things. But being 72 years old I want each episode to be as succinct as possible without unnecessary talk

I try and try to listen to your video but you go off on a tangent too much. Six minutes into the video and you have not begun solving yet. Would love to learn from you but you just talk and talk and talk and ...................................

I eyeballed it at 4. When you said 2 answers I paused and double checked that 8 would also work.

You drag it out too long.

To add fractions you need a common denominator like you were taught in 7th grade. To do this make the common denominator 4 * x. Then multiply each term by one to get (x/4 * x/x) + (8/x * 4/4) = 3 to get the equation (x^2 + 32) / 4x = 3 . Then multiply both sides by 4x to get x^2 + 32 = 12x and put equation in standard form of x^2 - 12x +32 = 0 . Then factor to (x - 4)*(x - 8) = 0 to get the answer of 4, 8. There is no need to find the lowest common denominator or to multiply the whole equation my some magic LCD of 4*x*1.

The answer is x=4 and/or x=8. It's simple by doing it in steps. The first step is subtract 8/x from each side of the equation, so x/4 = 3 - 8/x The next step is to multiply both sides by 4 so x = 4(3 - 8/x) or 12 - 32/x Then multiply each side by a factor of x. X^2 = 12x - 32 Then isolate the equation to one side. X^2-12x+32=0 This factors out to (x - 4)(x-8)=0 or x=4 and/or x=8

Yes it is x=4 and x=8 both work, took me 2 minutes in my head. Step 1 common denominator (4x) x^2/4x +8(4)/4x = 3. Step 2 multiply both sides by 4x, x^2 + 32 = 3(4x) then x^2 + 32 = 12x. Step 3 subtract 12x from both sides x^2 - 12x + 32 = 0. Step 4 factor (x - 4)(x - 8) = 0. Step 5 solve for x in each set x - 4 =0, x - 8 =0. Step 6a add 4 to each side in x - 4 = 0 x - 4 + 4 = 0 + 4, x=4 Step 6d add 8 to both sides in x - 8 = 0, x - 8 + 8 = 0 + 8 x=8 Step 7 test results by substituting results in origional equation. A. 4/4 +8/4 = 3 1 + 2 = 3, 3 = 3,B. 8/4 + 8/8 = 3, 2 + 1 = 3, 3 = 3. Conclusion both 8 and 4 are solutions for x.

4 was the first number that made any sense in my mind and without having much of an understanding of algebra or the other methods used to solve this problem.

X = 8 or x = 4

This is always where I got in trouble in school. They always wanted to show the work. They wanted to see how we solved it. That takes too long. I just look at the problem and my brain figures out the answer. This happens almost instantly

x/4 + 8/x = 3 Let t = x/4 t + 2/t = 3 t^2 -3 t + 2 = 0 (t -1)(t-2) = 0 x = 4 t x = 4 Or x = 8

You should always use the quadratic equation. When I discovered the quadratic equation I was mad that math teachers wasted my time with factoring.

If X squared over 4X + 32 over 4X = 3, then cross multiplication would mean that X squared + 32 = 3(4X), simplified to X squared + 32 = 12X. Then X squared minus X + 32 = 0. It then becomes (X-4)(X-8)=0. X-4=0, then X = 4. X - 8 = 0, then X = 8.

x/4 + 8/x = 3 -> x^2/4x + 32/4x - 3 = 0 -> ((x/2+32)/4x) - 3 = 0 -> x^2-12x+32 (Quadratic equation) Given this quadratic equation we can solve for solutions to x using the quadratic formula: (-b+-sqrt(d))/2a where d=b^2-4ac is the discriminant to the quadratic equation: x = (-b+-sqrt(b^2-4ac))/2a = (-(-12)+-sqrt((-12)^2-4*1*32))/2*1 = (12+-sqrt(16))/2 = 6+-2 The discriminant (16) is greater than 0 so we get 2 solutions: x1=6+2=8 x2=6-2=4 Intuitively the solution could also have been found by simply looking at the equation x/4 + 8/x = 3 and realizing that probably the solutions are 4 and 8 by substituting into x and doing a bit of simple math: 4/4+8/4=3 as well as 8/4+8/8=3. With more complex equations and/or unintuitive values of x the best method is to use formula for the discriminant and the quadratic formula.

I am happy to inform you that your lessons have produced solid results. 6 months ago I would have given up on this one and now I can solve it using algebra. Now I'll watch the video to see if my method was the right one but I'm confident it was. :) Thanks!

(x/4)+(8/x)=3 therefore x not= 0 x × {(x/4)+(8/x)=3} x^2/4+8=3x 4×{x^2/4+8=3x} x^2+32=12x x^2-12x+32=0 note => 2 solutions for x but not 0 the quadratic equation: [-b +/-sqrt(b^2-4ac)]/2a for x^2-3x+8=0 a=1 b=-12 c=32 so [-b +/-sqrt(b^2-4ac)]/2a [12+/-sqrt(144-128)]/2 [12+/-sqrt(16)]/2 [12+/-4]/2 sol.1 x=4 sol.2 x=8 verify (x/4)+(8/x)=3 sol.1 x=4 4/4 +8/4=?3 1+2=❤3✔️ sol.2 x=8 8/4+8/8=?3 2+1=❤3✔️

The key to solving is to get all of the terms under a common denominator. The result is a quadratic equation in the numerator, which is easily factored into the two solutions.

You are bringing back lots of teaching I have had. My first algebra class was 1965!!! Thank you!!

To solve the equation x/4 + 8/x = 3, we can first multiply both sides of the equation by 4x to eliminate the fractions. (x/4 + 8/x) * 4x = 3 * 4x x^2 + 32 = 12x Next, rearrange the equation to set it equal to zero: x^2 - 12x + 32 = 0 Now, we can factor this quadratic equation: (x - 8)(x - 4) = 0 Setting each factor equal to zero gives us the possible solutions for x: x - 8 = 0 or x - 4 = 0 x = 8 or x = 4 Therefore, the solutions to the equation x/4 + 8/x = 3 are x = 8 or x = 4.

No need for complicated algebra. Use cross reduction and you get 1+2=3. The X’s cancel each other out, 4 and 8 a divisible by 4 leaving you with 1 over 1 and 2 over 1.

Mental math 101. Look, think, solved it! Something + something = 3. Answer: 4 😊

I really like your video. You are very thorough and try to point out the complexities by referring to many points of solving the equations. Yes it may seem tedious but it helps me. I still have some trouble knowing when I need to look for lowest common multiplier versus lowest common denominator. I think it takes a lot of patience and determination to get good at this stuff. I am a biologist and though I've had some training in math, I was always kind of slow, but usually I could get through the courses with a good grade. Now I am retired and I find it a fun game to redirect my attention to algebra and other math, so I hope you and I will keep enjoying the challenges. Keep up the good work, and best wishes!

It's simple enough, that I don't need to create the full quadratic equation. The mean of the roots is 3 (constant term) * 4 (recibrocal of linear term) / 2 = 12/2 = 6. Obviously x = 4 and x = 8 result in 1+2 or 2+1, both are 3. Or you calculate 8 (1/x term) * 4 (see above) = 32 = x_1 * x_2. Or you take the long way with x^2 - 12 x + 32 = 0 => x = -(-12)/2 +/- sqrt(36 - 32) = 6 +/- 2.

Thank you for taking the time to explain! I am enjoying the learning process!

In Hong Kong, some primary students can complete this simple calculation. I used to educate Olympic math and eye level. Some primary students can handle this easily

I think I knew this sinds 1962: solution x =4 and x=8; by writing first part as the sum with the common denominator 4x and multiply by 4x you get the quadratic equation:ax^2+bx+c= x^2-12x+32=0; D=b^2-4ac; x=(-b±√D)/2a (D is the Discriminant)

X=4 & 8. Did it in my head & within a few minutes.

Thank you for your service. I was denied the honor in 1976 due to being an Epileptic, but so grateful to those that can and do

At 08:45 you have obviously decided to make the process as complicated as possible. I was able to solve this by simply looking at it for a few seconds.

For some reason I arrived at 4 and 8 but differently. I moved the 8/x to the other side resulting in x/4 = 3 - 8/x, which becomes x/4 = (3x - 8)/x. Cross-multiplying gets me x^2 = 12x - 32, which becomes the same quadratic equation you have of x^2 - 12x + 32 = 0. Factored out that leads to 4 and 8.

formula for roots of a quadratic equation X**2 -12X + 32 = 0 (which we get when multiplying each element with 4X) gives us 8 and 4 as 2 roots of X

x=8 8/4=2 + 8/8=1 2+1=3 (Edited to add): x could also be 4 4/4=1 + 8/4=2 1+2=3

Gleichung mit 4x Multiplizieren --> x^2 - 12x + 32 = 0 Quadratische Ergänzung ergibt --> ( x - 6 )^2 = 4

You're a great teacher. Keep doing what you're doing.

got it 4 & 8 solved by sight easy calculation had to be 2 + 1 and 1 + 2 thanks for the fun

Guess and check is quickest in this case. I need 2 numbers that add up to 3. Hmmm 1+2=3. Looks like 4 works in that case. Algebra is not always needed, sometimes a little number sense can work.

Well, I did it by taking care of the fractions first and then used the cross product to solve the problem. At the end I came up with the right equation anyway i.e. x Squared + 32 = 12x Then I substracted 12x from both sides, factored and came up with (x -4) (x - 8) = 0 and voilà! But I could have done it by multiplying the whole equation by 4x as you did. When I see fractions and an (=) sign I always think cross product. ;)

This was a good one. I labored for a long time before finally realizing that I had to get that x out of the denominator. So here comes the quadratic equation, and it was simple to solve.

I did not even think about using lcd. I just multiplied both sides by x and right there you have a quadratic equation… And, while factoring this out is nice, I am lazy and would just plug it into the formula😎

If you have any problem as simple as this, and you are stuck after the using the LCD, I suggest trial and improvement . Clearly when x = 4, we are nearly there . Then do a long division to get the other factor, x-8. Then equate both factors to be equal to zero

The answer is x = 4, or x = 8, and is is simple - it's solvable by inspection. 4/4 = 1, 8/4 = 2, 1+2 = 3. And 8/4 = 2, 8/8 = 1, 2+1 = 3. If you must SOLVE it, just multiply through by 4*x: x/4 + 8/x = 3 x^2 + 32 = 12*x x^2 - 12*x + 32 = 0 (x - 4)*(x - 8) = 0 x = 4, x = 8 Q.E.D. It's just a quadratic - that's about as simple as it gets.

x/4 -3 = -8/x ==> 3x/12 -36/12 = -8/x (3x-36)/12= -8/x ==> 3x**2-36x=-96 3x**2-36x+96=0 (x-8)(x-4)=0 x=4, 8 it is very easy to solve it

He’s TEACHING slow enough for children & teenagers to grasp. I think many of you look at this to test yourself & memory which is not what it’s intended for. Unfortunately, many folks being paid as teachers in public school are not teaching to educate the kids or help them comprehend the information. I feel he has a real grasp on teaching.

Multiply by 4x to eliminate denominators. You get a quadratic; apply the quadratic formula. Or, even better, in this case the quadratic easily factors into a product of linear factors (x-4)(x-8).

Χ/4+8/χ=3=> (Χ*χ + 4*8)/4*χ=3=> Χ^2+32=3*(4*χ)=> Χ^2-12χ+32=0 Δ=β^2 -4*α*γ=> Δ=(-12)^2 -4*1*32=> Δ=144-128=16 Ρ1=(-β+sqΔ)/2*α= (-(-12)+sq16)/2*1= (12+4)/2=8 Ρ2=(-β-sqΔ)/2*α= (-(-12)-sq16)/2*1= 4 So x=4 or x=8

Replace the x with 4, solve 4/4=1; solve 8/4= 2; add 1+2=3 simple

Simplify the equation to the standadrd quadratic x^2 -12x+32=0; factorising you get (x-8)(x-4)=0. Hence X=8 or 4.

I had 4 and 8 on sight. I am a 61 year old British electronics engineer who mainly uses standard equations, calculus and FFT.

The general case is: (x / a) + (na / x) = (n + 1) That can be solved by applying this formula: x = (a / 2) [(n + 1) ± (n - 1)] Which is: S: { a ; na }

x/4 + 8/× = 3 = ? cruzando as duas frações, vem: x elv 2 + 4 X 8 / 4x = 3 x elv 2 + 32 = 12x x elv 2 - 12x + 32 = 0 que é uma equação do 2° grau a = x elv 2 = b = -12 c = 32 Dois números cuja soma seja - 12 e o produto seja 32. Ax + Sx + P =0 S = -4 + (-8 ) = - 12 P = -4 X (-8) = 32 Entoa as raizes da equação terão os sinais trocados: r1 = 4 e r2 = 8.

Super simple, I would expect a c student to get this right in less than 20 seconds. 1:) Bow tie method: (x² + 32) / 4x = 3 2:) get rid of fraction by multiplication: [(x² + 32) / 4x ] * 4x = 3 * 4x x² + 32 = 12x 3:) set equation equal to zero and solve via foil x² -12x + 32 = 0 (x-8)(x-4) = 0 x = 8 and x = 4. Like I said super simple if you know what you're doing.

I didn't bother to watch more than the first few minutes. It takes about a minute to solve it

How is it not so simple? It's an extremely standard exercise.

what software and devices do you use or your videos?

Thank you John, I appreciate your content.

Took me about 2 seconds to get 4 as an answer. But to do it on paper, we have x/4 + 8/x = 3. Multiply by 4x to get x^2 + 32 = 12x, or x^2 - 12x + 32 = 0, or (x - 8)(x - 4) = 0, so x = 8 and x = 4 are the answers. This could also be solved using the quadratic formula.

When solving equations you move terms from one side of the equals sign to the other and change the sign. Positive terms become negative, division becomes multiplication etc it is much more efficient.

After 50+ years of taking algebra, I got this with no problem. Easy peasy.

I am not sure, what is this about? it is a 10 seconds problem. x^2 + 32 = 12x (note x/= 0). x^2 -12x +32 = 0. (x-4)*(x-8) = 0. {x=4;x=8} It is longer to write then to solve it in ind, w/o paper!

Isn’t it 4 without even any solving? 😂😂

Because of algebra I know that x will be the same number and that there might be more than one choice. Basic knowledge of fractions told me that if I could get fractions equal to 1 and 2 it would work because 1+2=3 and 2+1=3. 4/4=1 and 8/4=2 so one solution is 4. 4/8=2 and 8/8=1 Therefore the second solution is 8.

I came up with 4 in a matter of seconds, when you said two solutions I came up with 8 quickly

I have to agree with Shelly. When I do one of your problems--I just skip ahead. In the words of my daughter when asked why she didn't want me to help with her math, she told her mother, "Mom, I don't want to know that much."

I multipled both sides of the equation by x to get the variable out of the denominator. Then you get a quadratic equation. I moved everything to one side of the equation so it’s equal to 0. Then I factored to get (x-8)(x-4)=0. So the solutions are 8 and 4.

Actually this problem is very easy to solve, as follows: X/4 + 8/X = (X^2 + 32)/4X = 3 X^2 + 32 = 12X X^2 - 12X + 32 =0, Now factor: (X - 8)(X - 4) = 0 X = 8, X = 4

Y=X/4， 2/Y=8/X，Y+2/Y=3， Y^2-3Y+2=0，（Y-1）（Y-2）=0， Y=（1，2）， X=（4，8）

I was able to get the answer by getting the right hand side of the equation equal to 0, then used the quadratic equation to solve it - got 2 answers, and both worked back in the original problem.

yes, 4 and 8 are easy and intuitive, but setting up a quadratic in a slightly different way gives x=6+2xsqrt(6) , and 6-2xsqrt(6) for two more solutions.

Great little problem, especially making sure that people check the answers actually work. Thanks for creating and sharing. I love your channel. However, I feel that it would be easier for people to understand if, rather than distributing by 4x, the fractions were both converted to 4x denominators then everything multiplied by 4x to produce the equation that becomes the quadratic. As usual with a lot of problems, always more than one way to solve and it’s about finding the method that works for the student.

What you are seeing is the schtick. He is an elite mathematician and wants to give you a real math experience. The "prollem" looks simple and turns out it is rife with pitfalls. You, therefore, can't solve it and he steps in step by step and solves it. This is how you learn math. If you want to play childhood T-ball, this is not the guy. He's gonna test you and, frankly, I like that. He also designs tests for a living, so he's going to know how folks get sidetracked. That is valuable information! Love, love, love this dude!

Without watching the video, this one is quite easy. You are allowed to multiply both members by any value without changing the equation. Let's do it by x. Which gives us 1/4 x^2 -3x +8 =0. ∆=b^2-4ac = 9 - 8 = 1. x1&2 = (-b +- √∆)/2a = (3 +- √1)/1/2 = 8 & 4.

X/4 + 8/x = 3 X^2/4x + 32/4x = 3 (X^2 + 32)/4x = 3 X^2 + 32 = 12x X^2 - 12x + 32 = 0 (X-4)(x-8) = 0 X = 4 , 8 ✅

x/4 + 8/x = 3 x²/4x + 32/4x = 3 x² + 32 = 12x x² − 12x + 32 = 0 (x − 4) (x − 8) = 0 x₁ = 4 ∨ x₂ = 8 𝕃 = {4, 8}

It is simple, if we state, that x is ot 0. In this case, we can multipl the equation withh 4x and get thhe quadratic equation. x^2-12x+32=0 which leads to the 2 solutions: x=6+-sqrt(4) x=4 or x=8 We can state, thhat x is not 0, because otherwise the term 8/x is undefined.

I didn't need algebra, I solved it in 10 seconds. 3 can only be 1 + 2 . so 4/4 + 8/4 = 1 + 2 = 3. I didn't try any other fractions, so I didn't think of using 8. Once we got to quadratic equations in math, I was lost. I've used algebra occasionally after high school for fun, but never a quadratic equation. Ain't no body got time for that.

Does it require so much time to solve/explain this?

I figured this out in my head. What numbers added together equal 3? 1 and 2. So the fractions have to equal either 1 or 2. So X can be either 4 or 8. Too bad that it takes such roundabout, convoluted methodology in order to prove this.

20 minutes for basically solving a quadratic equation: yeah, nah... Maybe next time!

So I switched denominators did the fractions and well x over x = 1 : 8 over 4 = 2 so 1+2= 3 : x/4 or x/8 is always = to 1 because both answers will be 4/4 or 8/8

Thank you, I am about to take college algebra and am a total beginner

Ovo je dobro za predškolski uzrast:On iznaju da je 1+2=3, ili 2+1=3, a iz toga je lako zaključiti koliko mora biti x

X/4 + 8/X = 3 Muktiply both sides by 4X Gives X² + 32 = 12X X² - 12X + 32 = 0 (X - 8) (X - 4) = 0 X = 8 or X = 4

I multiplied by 4x at the first step for convenience, brought all the terms to one side and factored. Took 3 or 4 lines to the solution.

Thanks for giving me a memorable question on algebra, the answer is x=4 or x=8, using factorisation after simplification to x²-12x+32, thanks for the reminder but i advise you to shorten your videos, 20 min for one question for one video is way to long even if it has two methods😊

Took one look to ralize straight away just a quadratic equation -multiply through by 4x to make it look normal. I didn'y bothering spending 20 minutes to watch the video.

Just needed 15 seconds to do this in my head. This could have been explained on the board in two minutes.

Within 5 seconds I saw 1+2=3. I knew 4/4=1 & 8/4 =2. Therefore x =4. Then I saw that it work with x being 8. Total time for both, less than 20 seconds.

Let's replace x/4 = y So y + 2/y = 3 y**2 - 3y + 2 = 0 y**2 - y - 2y + 2 = 0 y(y - 1) - 2(y - 1) = 0 (y - 1)(y - 2) = 0 y = 1 and y = 2 x = 4 and x = 8

x/4=a a+2/a=3 a^2-3a+2=0 a=1 or 2 x=4 or 8

Finally something that is easy. :) But no were did I do it correctly. :) x=4, 4/4 +8/4, 1+2=3

Excellent video!

Great content. How about just 1 tangent per video?

The CD is 4x. (x/4)÷4x =1 (8/x) ÷ 4x = 2 1+ 2 = 3. It's that simple!

Shalom to everyone Does the teacher John have work sheets. About 100 drrills per sheets ? Thanks.

I eyeballed this "difficult" problem and had a working value for x in 20 seconds. When the sum total is a low integer like 3, anyone can iterate the likely possibilities and solve for x without any of the complicated algebra you claim is "required." I did!

Stay on track!!! This is math, not history !

You explain to much which deviate from yr target.we don't have too much time to explain the problem.Pse shorten the explanation.

This problem is EXTREMELY SIMPLE!! The result MUST equal 3, and "X" must be the same number. In this case "X" = 4. So, 4/4 = 1 + 8/4 = 2 Guess what? 1 + 2 = 3 Kindergarten wasn't wasted on me.