# Math puzzler

**URL:** <https://boards.straightdope.com/t/math-puzzler/153368>\
**Category:** Factual Questions\
**Created:** [February 7, 2003, 2:29am UTC](https://boards.straightdope.com/t/math-puzzler/153368 "2003-02-07T02:29:38Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\
**Post date:** [February 7, 2003, 2:29am UTC](https://boards.straightdope.com/t/math-puzzler/153368/1 "2003-02-07T02:29:38Z")

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We are trying to determine the derivative of

y=(x^2)/(x-1)

I use the Quotient Rule to figure this out and always come up with y’=0"

y’=(f’g-g’f)/g^2

= ((2x)(x-1) - (1)(x^2))/x^2-2x+1  
= 2x^2-2x-x^2/x^2-2x+1  
= x^2-2x/x^2-2x+1

= 1 \* 0/1

Okay, I know I’m making an arithmetic error. What is it? Can I not cancel out x^2-2x?

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**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\
**Post date:** [February 7, 2003, 2:56am UTC](https://boards.straightdope.com/t/math-puzzler/153368/2 "2003-02-07T02:56:25Z")

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You’ve got x(x-2)/(x-1)(x-1).

None of that cancels out.

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**Author:** ![Hauky](https://avatars.discourse-cdn.com/v4/letter/h/0ea827/32.png) [@Hauky](https://boards.straightdope.com/u/Hauky)\
**Post date:** [February 7, 2003, 3:29am UTC](https://boards.straightdope.com/t/math-puzzler/153368/3 "2003-02-07T03:29:23Z")

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For reference, my TI-89 graphing calculator says the answer is:

y’ = x(x-2) / (x-1)^2

With the caveat that I haven’t done derivatives by hand for a while now, I quite simply cannot figure out what the heck you’re doing with that 1\*0/1 step. Where are you getting that from? Just factor out the step above that and it looks like you’ll get the answer my calc gives.

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**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\
**Post date:** [February 7, 2003, 3:31am UTC](https://boards.straightdope.com/t/math-puzzler/153368/4 "2003-02-07T03:31:29Z")

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It doesn’t cancel like that. What’s 4/(4 + 1) equal to? This is a pretty simple problem. I think if you just take a good, long look at it you’ll see what’s up.