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 ...................................

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...

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

Multiply everything by 4x... 4x² - 12x + 32 = 0 (x - 4)(x - 8) = 0 x = 4, 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.

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

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.

X = 8 or x = 4

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/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

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

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

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.

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

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. Did it in my head & within a few minutes.

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.

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

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.

I don't even know why... but, I found this challenge so satisfying... I actually remembered... I'm 1966. Thank you for the confidence boost. Makes me feel like I can help my grandkids.

(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✔️

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

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.

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

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

At <a href="#" class="seekto" data-time="525">08:45</a> 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.

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)

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. ;)

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 }

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

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.

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.

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

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😎

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!

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

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 -> 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.

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.

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.

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）

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}

辺々4xを掛けx^2+32=12x 12xを移項し(x-4)(x-8)=0 ∴x=4,8

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

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

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

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.

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).

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.

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

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.

4 and 8

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 John, I appreciate your content.

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.

x=8 and x=4 solves it.

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.

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 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.

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

This equation does not warrant 20-minute video. Noting that x is not equal to zero, reducing it to the common denominator and solving quadratic equation is a standard practice, no mysteries here. This equation is YES, so simple.

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

x^2-12x+32=0 x^2-4x-8x +32 =0 (x-4)(x-8) = 0 x = 4 or x = 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 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."

WE DON'T CARE HOW SMART YOU ARE - GET ON WITH IT!

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

Also solved at age 71.

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.

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.

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

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

Great content. How about just 1 tangent per video?

-> x^2-12x+32=0 , x^2-4x-8x+32=0 , (x-4)(x-8)=0 , x= 4 , 8 ,

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.

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

You finish my data with your long explaination

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.

Use LCD to get the variable out of the denominators. Good Stuff.

I instantly divided into c (each x turning into 1. 1x8=8 1x4=4 =8/4 =2 1+2=3

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.

Thanks Mr. KZfaq Math man.

<a href="#" class="seekto" data-time="244">4:4</a> =1 <a href="#" class="seekto" data-time="484">8:4</a> =2 1+2 + 3 Both X are 4 !

Yes I can solve it by looking at it. It does not take long. May be 20-30 seconds I don't know exactly I did not time myself.

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

Combine the fractions with a common denominator, multiply both sides by the common denominator, rearrange into a quadratic and factor. All of that I was able to do in about 29 seconds. It should not take 20 minutes and 14 seconds to explain that.

I solved it in one sec, just looking at the thumbnail as the notification of the video appeared.

This one is actually very simple. 2+1=3 and 8/4+8/8=2+1 so x=8.

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

Thank you

I was always bad in maths but I could solve it in less than 10 seconds just using my head

How on earth can you talk about such a simple problem for 15 minutes.....?

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!

It all results in an equation x² - 12x + 32 = 0 so (x-4).(x-8) = 0 and x = 4 or x = 8

If this isn't considered simple anymore we in trouble

Maxima quickly finds that only 2 answers exist: x=4 and x=8

Excellent video!