x minus x squared all over x squared minus x = ? Many will get this ALGEBRA problem WRONG! 

Got it right! I just plugged in a couple numbers and it came out to -1 both times.

You are a teacher with 630k students, so you have a responsibility to pronounce math terminology correctly. It's algebraic, not algebaric, so it's pronounced al-juh-bray-ic, not al-juh-bare-ic.

c) = (-1) is correct because the numerator is the negative of the denominator.

Unless I missed it, there's a rather important bit missing here: for two particular values of x, the expression in undefined because the denominator is 0. Anyone whose algebra skills extend to being able to factor x-x² to x(1-x) should be able to quickly see that the denominator equals -1 × the numerator so the answer must be -1. For finding out the answer, factoring is way more complexity and faff than you need. But the one reason it might be worth doing is to help see what values of x give 0 in the denominator. Again, anyone who can factor x²-x to x(x-1) should be able to quickly see that for x=0 and x=1 the denominator is zero. So the answer to the question is -1, provided than x≠0 and x≠1 You went through all the bother of factoring and then didn't actually use the factored version of the expression for the one thing it's useful for!

Factor top to -1(x^2 -x), cancel with bottom leaving -1

Well, there is a rule: A - B == - (B - A). This can be used to great effect.

I learned a lot from your RU-vid channel and videos and I what to say thank you 📓🖋🩷🩵❤️💜💖💗💓💕💞

-1 in about three seconds. Seriously? "MANY WILL GET WRONG" crap again? Can't you just teach without baiting? It's demeaning to those who are struggling. This is the reason people say, "Math is hard!" You put them down before they ever get the chance to learn. Telling them they're just part of the group who get the problem wrong only reinforces their anguish. Be human. Stop with that "MANY WILL GET WRONG" crap. Teach the math.

A 2 second mental solution X-X^2 = -1( X^2 - X ) The X^2 - X cancels out leaving -1 However, X=1 and X=0 are excluded because the denominator is 0.

MANY MISS THE POINT! The fundamental, primary issue before a student begins to work on this problem is to understand what the goal is. If this problem is given as homework where "show your work" is a necessity, then the explanation and calculation given by John Mr. Mathman is right on. HOWEVER, if this were a question from an SAT or similar standardized "fill the oval with a dark mark from a No. 2 lead pencil" test, the analysis shown would be a counterproductive and an unnecessary waste of time. On standardized tests the ONLY goal is getting the right answer, nothing else. For certain questions - like this one - the "random substitution" method works best: Pick a random number, plug it in for the variable, do the calculation, and compare your answer to the answer choices provided. If your calculated answer corresponds with ANY answer choice, that choice MUST be the right one. Done and done. If you distrust the method and have time, you can run another random number which should confirm your original answer. Since you're not charged with demonstrating a "proof" but, rather, only finding the answer, the easiest and quickest method is superior. If the goal, however, is to provide an opportunity to show your teacher that you understand HOW to derive correct answers, then the long and formal way is necessary. So I chose 13. Pretty random, and amenable to easy arithmetic calculations. So.... (13-13^2) / (13^2-13) = (13-169)/(169-13) = (-156)/(156) = -1. Since -1 IS the answer for 13, it must also be the answer for all numbers; no other answer choice satisfies 13, so all of the remaining choices are wrong. A nervous Nellie might confirm with a different number. Try -1/2. You get: [(-1/2) - (-1/2)^2] / [(-1/2^2) - (-1/2)] = [(-1/2) - (1/4)] / [(1/4)-(-1/2)], or (-3)4) / (3/4) which is -1. Written using decimals is easier to see: [(-0.5) -(-0.5^2)] / [(-0.5^2) - (-0.5)] = - 0.25 / 0.25 = -1. Same answer. The right one, whose acquisition is the only goal. Easy peasy and a real timesaver.

but only if x is not 0 and x is not 1.

Practice Practice Practice, very informative video

I think you over complicated the algebraic solution. Setting aside the fact that x = {0,1} yields an undefined solution, since that was not one of the multiple choices, for all other real number values of x, (1-x)/(x-1)=-1.

Solved in my head at the thumbnail in about 20 seconds, my answer is c) -1.

However if x=0, this results in 0/0 and you cannot divide by zero

Just multiply top and bottom by -1. -1 ( x - x²) (x² - x) 1 ____________ = _________ = _______. -1 (x² -×) -1 (x² - x) -1 (1) = -1

Please don't talk and waste in subscription matters come to point

(A+B) = - (B+A) right? I got the correct answer.

x - x^2 / x^2 - x So let’s start out by realizing that if x is zero then this is undefined so x cannot be zero We can alter the denominator and the numerator I am going to multiply the numerator by -1 so -1 * (x - x^2) = -1(-x + x^2) = -1( x^2 - x) -1* (x^2 -x) / (x^2 - x) = -1 So looking up you have -1 as the answer But is this the only way to solve the equation We can move 1x from the equation. (1-x)/(x-1) = k (1-x) = k(x-1) 1- x - kx + k= 0 1 + k - x(1+k) = (1-x)(1+k)=0 solutions are x=1, k = -1

original form: y = (x - x²) / (x²-x) 1) we have a GCF of x so: y = [ x (1 - x) ] / [ x ( x - 1)] 2) we have 1 - x in numerator and x - 1 in denominator so lets write it so they are exactly the same inside the ( ): y = [ x (1 - x) ] / [ - x (1 - x)] 3) Now we can cross cancel as the ( ) portion is exactly the same this gives us: y = x / - x this means y must equal -1 proof of step 2: y = x ( 1 - x ). This equals the original numerator of (x - x²) y = -x ( 1 - x). This equals -1x + x². If you remember that a - b is the same as -b + a then we know that -x + x² is the same as x² - x. This means the denominator is the original denominator. Super simple if you remember and fully understand the rules of addition and subtraction when it comes to numbers with opposite signs.

Suppose x=0 or 1. Then what?#!

John, It seems that, in the second part of the video, everything gets cancelled. But I can't see the result being 1. You crossed the whole fraction. Cansomeone help me with this,please? Thanks

Math lover.-x divided by x=-1

For X≠1 and X≠0 : -1. The proposed answers are not complete as they don't include the undefined cases. IF X=0 OR X=1, then, you get 0/0. That's undefined or Not a Number (NaN)

Ans=--1. --1(x^2--x)/(x^2--v)=--1

Hi, please excuse my bad English, 0 and 1 and -1 all fit by filling in, but calculating the solution is only -1😵‍💫 i m puzzled Greetz from Germany

Is always worth to substitute the x in your mind before engaging in something more laborious. Here making the x simply 2 solves the sentence: x = -1

Factoring out x in top and bottom gives: x(1 - x)/x(x - 1) x in num cancels x in denom leaving: (1 - x)/(x - 1) = -(x - 1)/(x - 1) x - 1 in num cancels x - 1 in denom leaving -1. Answer is: -1 =

X^4-X^2

Before watching. Factor x out top and bottom. Look at the denominator and determine the domain. X cannot be 0, or 1, or one would end up dividing by 0, which without a lim in front is a no-no. That leaves answers c and d, so 50% chance to guess correct from here. Now, since we can now cancel the x/x part, playtime starts. Is there anything to be done to divide (1-x)/(x-1)? Yes, multiply top, or bottom, not both 😃, by -1, and switch signs in the brackets to compensate for the introduction of the -1. Now the answer should be clear since one ends up with -1/1 or 1/-1, both result in -1, I.e the answer should be c. Now let’s watch🤓after watching, yes, if you have no clue, guess, but know how the teacher/prof scores. I had one prof who would deduct points for wrong answers. This changes the math on guessing a lot! And I love that I guessed the term ‘no-no’ 😎 but, I disagree that one cannot/ should not cancel the x/x at the earliest opportunity. No need to drag terms around beyond when they can just ‘go away’.

Got it right can't believe it Mr J ❤ 👋💪🙏🌎 This is the good stuff I have a serious math problem 😂 I'm addicted to math

-1. Is the answer

I factored. Then I put In several values for x. They all worked out to negative one

Also got it right, but it took a few minutes and some serious thinkin'. But before these videos, I might have been totally lost.

X^2 - X = -1 * ( X - X^2) in the denominator. It cancels out leaving 1 / -1

Thanks Mr Mathman. The channel helps me remember how to learn. Thankyou for the effort.

Answer X = - 1

Thank you john

Yay! I got it right! Love your challenges!❤🧮➖➕

c) -1

C = -1

c) -1

C -1

-1÷1 = -1

C

C

C

Thanks. Happy to report that I got it right first time.

factor the negative....great thanks for the fun

_1

-1

-1

-1

_1

1

1

The answer is “None of the above”. This is still a function of X so it depends on what you plug in for X. The answer is -1 for most values of X and “Undefined” for x = 0 or x = 1.

You're a great teacher.

Tricky

Thank you

Nice

x/2

Letters can never equal numbers!

c) -1 AND a) 0. I have to disagree with the basic rule that a fraction's denominator can never be zero. I hereby declare that it CAN be zero when the numerator is also zero. So 0/0 =0. In this special case, you CAN divide by zero because nothing divided by nothing is nothing. That is intuitively correct. If the numerator is any number other than zero, the rule is true. Therefore answer a) 0 is also correct, when X = 0.

One for the kiddies: If you take 3 smarties and divide by nothing what do you have? STILL 3 SMARTIES! (.munch.munch. ☺️😋) If it's -2 outside and the weather man says it is going to get warmer by one-half, what is the temperature going to be? -1 🎉. TA-DA! 🎉