## How would you simplify this

For the discussion of math. Duh.

Moderators: gmalivuk, Moderators General, Prelates

Posts: 357
Joined: Mon Aug 20, 2007 5:59 pm UTC

### 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
Guys guys guys! I found Russel's teapot! . . . nevermind, it was just Jesus flying to Mars again.

SimonM
Posts: 280
Joined: Sat Jul 21, 2007 4:49 pm UTC
Location: Guernsey, CI
Contact:

### 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?

Posts: 357
Joined: Mon Aug 20, 2007 5:59 pm UTC

### 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.

SimonM
Posts: 280
Joined: Sat Jul 21, 2007 4:49 pm UTC
Location: Guernsey, CI
Contact:

### Re: How would you simplify this

Not the point, I'm sorry
mosc wrote:How did you LEARN, exactly, to suck?

Buttons
Posts: 858
Joined: Wed May 02, 2007 3:27 pm UTC
Location: Somerville

### Re: How would you simplify this

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

Posts: 357
Joined: Mon Aug 20, 2007 5:59 pm UTC

### Re: How would you simplify this

all right

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...
Irrational (?)
Posts: 2413
Joined: Thu Jan 18, 2007 12:05 am UTC

### Re: How would you simplify this

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

Posts: 357
Joined: Mon Aug 20, 2007 5:59 pm UTC

### 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?
Guys guys guys! I found Russel's teapot! . . . nevermind, it was just Jesus flying to Mars again.

xprisoner
Posts: 10
Joined: Mon Oct 01, 2007 4:20 am UTC

### Re: How would you simplify this

Q: How would I simplify this?

A: Software (Maple)

korhonenpt
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.

Posts: 357
Joined: Mon Aug 20, 2007 5:59 pm UTC

### 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.

Mouffles
Posts: 60
Joined: Fri Jul 06, 2007 10:02 am UTC
Location: New Zealand

### Re: How would you simplify this

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.

antonfire
Posts: 1772
Joined: Thu Apr 05, 2007 7:31 pm UTC

### 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.
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?

Posts: 357
Joined: Mon Aug 20, 2007 5:59 pm UTC

### 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
Factoids are just Datas that haven't grown up yet
Posts: 5967
Joined: Tue Nov 28, 2006 9:50 pm UTC
Location: Sydney

### Re: How would you simplify this

Ever heard of maxima?
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

Yesila
Posts: 221
Joined: Sun Dec 16, 2007 11:38 am UTC

### Re: How would you simplify this

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.

antonfire
Posts: 1772
Joined: Thu Apr 05, 2007 7:31 pm UTC

### 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.
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?

Infornographer
Dick-in-a-Casserole
Posts: 389
Joined: Sun Sep 16, 2007 7:35 pm UTC
Location: Boston, MA

### Re: How would you simplify this

This problem has a particularly elegant solution using matrices...
(Formerly Gnophilist)

Posts: 357
Joined: Mon Aug 20, 2007 5:59 pm UTC

### 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.

antonfire
Posts: 1772
Joined: Thu Apr 05, 2007 7:31 pm UTC

### 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.)
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?

Posts: 357
Joined: Mon Aug 20, 2007 5:59 pm UTC

### Re: How would you simplify this

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.

antonfire
Posts: 1772
Joined: Thu Apr 05, 2007 7:31 pm UTC

### Re: How would you simplify this

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?

Posts: 357
Joined: Mon Aug 20, 2007 5:59 pm UTC

### 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.
Guys guys guys! I found Russel's teapot! . . . nevermind, it was just Jesus flying to Mars again.

scarletmanuka
Posts: 533
Joined: Wed Oct 17, 2007 4:29 am UTC
Location: Perth, Western Australia

### Re: How would you simplify this

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.

antonfire
Posts: 1772
Joined: Thu Apr 05, 2007 7:31 pm UTC

### 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?