How would you simplify this
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How would you simplify this
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
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
Guys guys guys! I found Russel's teapot! . . . nevermind, it was just Jesus flying to Mars again.
Re: How would you simplify this
I suggest no one helps him until after the 17th
mosc wrote:How did you LEARN, exactly, to suck?
Re: How would you simplify this
I had to mail it by today
Guys guys guys! I found Russel's teapot! . . . nevermind, it was just Jesus flying to Mars again.
Re: How would you simplify this
Aradae wrote:I had to mail it by today
Not the point, I'm sorry
mosc wrote:How did you LEARN, exactly, to suck?
Re: How would you simplify this
But other people can still read this and mail it out today. Let's wait until tomorrow.
Re: How would you simplify this
all right
edit: i finally got it
edit: shit, nevermind I don't have it
edit: i finally got it
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.
 3.14159265...
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Re: How would you simplify this
WTF! HOW DID I NOT HEAR ABOUT THIS!
I always miss out on shit
I always miss out on shit
"The best times in life are the ones when you can genuinely add a "Bwa" to your "ha"" Chris Hastings
Re: How would you simplify this
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?
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.
Re: How would you simplify this
Q: How would I simplify this?
A: Software (Maple)
A: Software (Maple)

 Posts: 32
 Joined: Sat Nov 24, 2007 4:29 am UTC
Re: How would you simplify this
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.
Edit: ahh, i have a pretty good idea. Won't say anything till aget the 17th, though.
Re: How would you simplify this
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.
Guys guys guys! I found Russel's teapot! . . . nevermind, it was just Jesus flying to Mars again.
Re: How would you simplify this
Done it. It's a very elegant problem.
Also, this. It's very useful to know the answer before you start something like this.xprisoner wrote:Q: How would I simplify this?
A: Software (Maple)
In the spirit of taking things too far  the 5x5x5x5x5 Rubik's Cube.
Re: How would you simplify this
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.
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.
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?
Re: How would you simplify this
I don't have maple
Guys guys guys! I found Russel's teapot! . . . nevermind, it was just Jesus flying to Mars again.
 jestingrabbit
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Re: How would you simplify this
ameretrifle wrote:Magic space feudalism is therefore a viable idea.
Re: How would you simplify this
I feel that the actual answer should be in the lines of an essay discussing how illposed 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 xvalues 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.
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 xvalues 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.
Re: How would you simplify this
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.
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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 DickinaCasserole
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Re: How would you simplify this
This problem has a particularly elegant solution using matrices...
(Formerly Gnophilist)
Re: How would you simplify this
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)
Guys guys guys! I found Russel's teapot! . . . nevermind, it was just Jesus flying to Mars again.
Re: How would you simplify this
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.)
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?
Re: How would you simplify this
you're fucking kidding me
all this time the answer was a + b + c + d
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.
Re: How would you simplify this
Indeed.
Now I wanna see Gnophilist's solution with matrices.
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?
Re: How would you simplify this
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.
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
I don't see why you have to break the 4.
Spoiler:
Re: How would you simplify this
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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