Watch me solve this Rational Equation - step-by-step

[@tomtke7351]

I'd guess a bit of substitution might be helpful as in substitute Y = (1/(1+x)) so that 6Y^2 - Y = 1

[@b213videoz]

This is exactly what I did 😉

[@mr.mxyzptlks8391]

Exactly what my first instinct was, substitute…

[@padraicbrown6718]

I got 1 through inspection; and realise that it is a QE and would have another solution. I shall watch to review this kind of equation! .... and got it! Thanks Mr KZbin Math Man!

[@ΘωμάςΓκλεζάκος]

just: Let a = 1/(x+1). Then you have to solve 6a^2-a=1 that is 6a^2 -a -1=0, Discriminant = 25, a=1/2 or a=-1/3, that is x=1 or x=-4

[@panlomito]

This is exactly what I did, very clean and simple, I don't understand why you would make such a hustle of this equation.

[@EdwardCurrent]

@@panlomito It'd be cool to show both methods. Math is beautiful how different journeys lead to the same destination

[@panlomito]

@@EdwardCurrent True, but I prefer short cuts when available.

[@MartinHermans-dw3is]

I subbed in 'u' for 1/1+x and then factored that. solving for both solutions, i put u = 1/1+x and entered the two values for u and got my two answers

[@EdwardCurrent]

I don't remember learning this in high school (multiplying by an LCD involving variables), very cool.

[@Kleermaker1000]

Watch me solve step by step, using the proportion method. :) 6(1/x + 1)^2 - (1/X + 1) = 1 => 6(1/x^2 + 2X + 1) - (1/X + 1) = 1 => 6/(X^2 + 2X + 1 - (1/X + 1) = 1 => 6(X + 1) - 1(X^2 + 2X + 1)/(X^2 + 2X + 1)(X + 1) = 1 => 6X + 6 - X^2 - 2X - 1/(X^2 + 2X + 1)(X - 1) = 1 => 6X + 6 - X^2 - 2x - 1 = (X^2 + 2X + 1)(X + 1) => 6X + 6 - X^2 - 2x - 1 = X^3 + 3X^2 + 3X + 1 => - X^2 + 4X + 5 = X^3 + 3X^2 + 3X + 1 => - X^3 - 4X^2 + X + 4 = 0 => - (X^3 + 4X^2 - X - 4) = 0 => X^2(X + 4) - 1(X + 4) = 0 => (X^2 - 1)(X + 4) = 0 => (X - 1)(X + 1)(X + 4) = 0 => X = 1 and X = - 4 (X = - 1 is not a solution, because dividing by 0 is not allowed and 1/- 1 + 1) = 1/0: not possible!).

[@MargaretCutt-um8iq]

I had an "ah ha! L" moment with this. I am refreshing my very very very rusty algebra skills with your classes. Phew!

[@russelllomando8460]

good one, thanks

[@stuartyoung5728]

The , equation can be solved as a quadratic in 1/(x+1).

[@erniedichiarafromminecraft7990]

Why not use substitution for y = 1/ x + 1 then Factor

[@devonwilson5776]

Greetings. We must realize that X has two values, and the values are 1 and minus 4. From the expression given we have (6-(X+1))/(X+1)^2=1. Moving on, we have 6-X-1=X^2+2X+1, and 5-X=X^2 +2X+1 is reduced to X^2 +3X-4=0 after transposing and adding and subtracting like terms. Now, we will simply factor the expression X^2+3X-4=0 to get (X+4)(X-1)=0 from which it is determined that X =1 or -4.

[@williamBryan-k2e]

this is how I did it, but made some math errors 6 -(x+1) I made into x+5 , not -x + 5. Once fixed, I got it right.

[@b213videoz]

Much to my surprise I managed to solve it. In fact it's nowhere this intimidating that it appears to be. The trick is to introduce a variable. 1 let t = --- x+1 6t² - t - 1 = 0 t1 = - 1/3 1 1 --- = ---; x+1 = -3; x = -4 x+1 -3 t2 = 1/2 1 1 --- = ---; x+1 = 2; x = 1 x+1 2

[@janetdavis4724]

This should only be used in college , most people in high school don’t use this after they graduated..

[@MrSummitville]

The students that will have an engineering job may need to learn this in the 10th grade. The engineers work hard, so you don't have to.

[@MaydayAggro]

Had to use paper this time but got it quickly using y = 1/(x+1).

[@Jesus-The-Everlasting-Father]

He talks a lot to make his video longer. Everyone, there is another video that is very clear and short in explanation. I will link it here.

[@leetrask6042]

Why do we call it a quadratic equation when quad seems to imply something related to four? Shouldn't it be called a bidratic equation?

[@rachaelcaruso7096]

I believe - it’s been many decades - my math teacher told me it’s graphed on the graph with four quadrants

[@ItsVideos]

@@rachaelcaruso7096 As are linear equations.

[@MrSummitville]

@leetrask6042 - The Latin root meaning of the word is ... to square.

[@1961ebutuoy]

No idea on correct method. But x = +1, worked.

[@gregc.mariano9226]

X= -4 &1

[@thomasroberts102]

X=5

[@brocksprogramming]

I got this one wrong.❤🎉

[@bobwineland9936]

No i just watch and study alot of math videos lol

[@ejcrispin]

Does this got bug any of you with his over talking? Im otta here.