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

How to solve a rational equation and check for extraneous solutions.
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[@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 😉

[@user-xy2wq1qn9p]

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

[@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!

[@EdwardCurrent]

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

[@stuartyoung5728]

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

[@russelllomando8460]

good one, thanks

[@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!

[@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.

[@user-cg5xv4zz2b]

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.

[@MaydayAggro]

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

[@janetdavis4724]

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

[@1961ebutuoy]

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

[@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

[@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.

[@createinmeacleanheartohgod6871]

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.

[@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.