How would you simplify this

For the discussion of math. Duh.

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Aradae
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How would you simplify this

Postby Aradae » Sat Dec 15, 2007 4:39 pm UTC

This contest has been frustrating me.

I got the other two questions but the first one I just mailed as far as I can go.

How would you simplify the fraction in the first problem?

http://webpages.shepherd.edu/rrajaram/M ... st2007.pdf
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SimonM
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Re: How would you simplify this

Postby SimonM » Sat Dec 15, 2007 4:44 pm UTC

I suggest no one helps him until after the 17th
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Aradae
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Re: How would you simplify this

Postby Aradae » Sat Dec 15, 2007 4:47 pm UTC

I had to mail it by today
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SimonM
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Re: How would you simplify this

Postby SimonM » Sat Dec 15, 2007 4:53 pm UTC

Aradae wrote:I had to mail it by today


Not the point, I'm sorry
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Buttons
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Re: How would you simplify this

Postby Buttons » Sat Dec 15, 2007 4:53 pm UTC

But other people can still read this and mail it out today. Let's wait until tomorrow.

Aradae
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Re: How would you simplify this

Postby Aradae » Sat Dec 15, 2007 4:54 pm UTC

all right

edit: i finally got it :P

edit: shit, nevermind I don't have it :(
Guys guys guys! I found Russel's teapot! . . . nevermind, it was just Jesus flying to Mars again.

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3.14159265...
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Re: How would you simplify this

Postby 3.14159265... » Sat Dec 15, 2007 9:45 pm UTC

WTF! HOW DID I NOT HEAR ABOUT THIS!

I always miss out on shit :(
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Aradae
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Re: How would you simplify this

Postby Aradae » Sat Dec 15, 2007 10:16 pm UTC

It's a relatively new contest (the first one they had was last year) only for high school students.

anyways, now that the post office is closed and the mail has been picked up, mind enlightening me on the method you'd use to solve it?
Guys guys guys! I found Russel's teapot! . . . nevermind, it was just Jesus flying to Mars again.

xprisoner
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Re: How would you simplify this

Postby xprisoner » Sun Dec 16, 2007 12:13 am UTC

Q: How would I simplify this?

A: Software (Maple)

korhonenpt
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Re: How would you simplify this

Postby korhonenpt » Sun Dec 16, 2007 12:36 am UTC

I think by factoring somehow and cancelling. I'm not sure to as exactly how though

Edit: ahh, i have a pretty good idea. Won't say anything till aget the 17th, though.

Aradae
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Re: How would you simplify this

Postby Aradae » Sun Dec 16, 2007 1:07 am UTC

:(

I've been working this for a week (my teacher didn't tell me about it till last Monday so I was kind of at a disadvantage). Though it says the 17th on there, what's the harm helping me today. The work has to be postmarked by today, there's no way me or anyone can mail the answer.

At the very least give me an answer so I can work out how to get that answer myself.
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Mouffles
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Re: How would you simplify this

Postby Mouffles » Sun Dec 16, 2007 6:00 am UTC

Done it. It's a very elegant problem.
xprisoner wrote:Q: How would I simplify this?

A: Software (Maple)
Also, this. It's very useful to know the answer before you start something like this.
In the spirit of taking things too far - the 5x5x5x5x5 Rubik's Cube.

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antonfire
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Re: How would you simplify this

Postby antonfire » Sun Dec 16, 2007 7:06 am UTC

Hints:

Write (a+b+c+d) as s (it makes life a bit easier).

Rewrite the top into four terms of (something/something+1), pull the 1 into the fraction. Stare.
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Aradae
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Re: How would you simplify this

Postby Aradae » Sun Dec 16, 2007 7:20 am UTC

I don't have maple
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jestingrabbit
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Re: How would you simplify this

Postby jestingrabbit » Sun Dec 16, 2007 7:29 am UTC

Aradae wrote:I don't have maple


Ever heard of maxima?
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Yesila
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Re: How would you simplify this

Postby Yesila » Sun Dec 16, 2007 11:57 am UTC

I feel that the actual answer should be in the lines of an essay discussing how ill-posed the question is. In short to actually be able to "Simplify" one needs a context. Without knowing what the expression is to be used for this may already be the "simplest" form.

For example consider the following two representations of the same function: f(x)=3x^2 + x, and f(x)=x(3x + 1). Now consider trying to find the x-values that satisfies f(x)=0, and then the solutions to f(x)=x. Most people would agree that to solve the first problem 3x^2+x=0 one should "simplify" the left hand side and consider x(3x+1)=0. On the other hand if one starts with the second problem in the form x(3x+1)=x most would "simplify" the left hand side and consider 3x^2 +x =x. So what "simplify" means is dependent on the context.

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antonfire
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Re: How would you simplify this

Postby antonfire » Sun Dec 16, 2007 12:01 pm UTC

You're right, but in this case, there is little ambiguity about what the simplest form is, and certainly no reasonable person would say that the form given is the simplest. That becomes clear once you solve the problem.

If someone really wants to see the solution rather than working it out for emself, I'll post it. Otherwise, I can just give more hints, I suppose.
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?

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Infornographer
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Re: How would you simplify this

Postby Infornographer » Sun Dec 16, 2007 4:12 pm UTC

This problem has a particularly elegant solution using matrices...
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Aradae
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Re: How would you simplify this

Postby Aradae » Sun Dec 16, 2007 4:16 pm UTC

no, I can work it out, I just need one more clarification. By "something" do you mean they are both the same "something"? I got them to the form 1 / ((s/2a) + 1)
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antonfire
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Re: How would you simplify this

Postby antonfire » Sun Dec 16, 2007 4:19 pm UTC

No, they're different somethings.

Each term looks like (x/y)+1, which you can turn into (x+y)/y, which simplifies. (The "+1"s come from the 4 at the end, if that wasn't clear.)
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?

Aradae
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Re: How would you simplify this

Postby Aradae » Sun Dec 16, 2007 11:11 pm UTC

you're fucking kidding me

all this time the answer was a + b + c + d
Guys guys guys! I found Russel's teapot! . . . nevermind, it was just Jesus flying to Mars again.

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antonfire
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Re: How would you simplify this

Postby antonfire » Sun Dec 16, 2007 11:13 pm UTC

Indeed.

Now I wanna see Gnophilist's solution with matrices.
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?

Aradae
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Re: How would you simplify this

Postby Aradae » Sun Dec 16, 2007 11:49 pm UTC

god, I wasted 5 days multiplying those fractions, trying to find a pattern and I honestly would have never thought to break that 4.

Ah well, though I may not have won $500 at least now I've got a better approach to problems like these.
Guys guys guys! I found Russel's teapot! . . . nevermind, it was just Jesus flying to Mars again.

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Re: How would you simplify this

Postby scarletmanuka » Wed Dec 19, 2007 1:45 am UTC

I don't see why you have to break the 4.
Spoiler:
I just rewrote a/(s-2a) as (-1/2 + s/2/s-2a), and similarly for the others. Then the numerator breaks into one piece which is s times the denominator, and one piece which is 2(-1/2 - 1/2 - 1/2 - 1/2) + 4 = 0.

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antonfire
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Re: How would you simplify this

Postby antonfire » Wed Dec 19, 2007 2:25 am UTC

Well, you certainly don't have to. There's more than one way to solve the problem.
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?


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