Question about SDMB's "No homework questions" policy re math questions specifically

[kaylasdad99]

@Johnny L.A.

This equation was in GQ in a thread that was closed down by Samclem:

    1         +        3        =       4
----------         ----------          ---
  x[sup]2[/sup] - 4             x + 2              5

Here’s the thing: I haven’t had to work such a problem since high school, which was over two decades ago. I simply don’t remember the “rules” for solving it. I e-mailed Samclem for a solution, since he’s the one who closed the thread; but I haven’t heard back from him.

I am not a student, and this is not homework for me.

But I’d still like to know the solution.

I’D like to know what all the fuss is about.

You know that the denominator for both fractions HAS to be 5.

Therefore x[sup]2[/sup] - 4 = x + 2 = 5

if x + 2 = 5, then x = 3

Sure enough, [(3 x 3) - 4] = 5.

So why all the Sturm und Drang mit der hohenmathematischen?

[ultrafilter]

@kaylasdad99

I’D like to know what all the fuss is about.

You know that the denominator for both fractions HAS to be 5.

Therefore x[sup]2[/sup] - 4 = x + 2 = 5

if x + 2 = 5, then x = 3

Sure enough, [(3 x 3) - 4] = 5.

So why all the Sturm und Drang mit der hohenmathematischen?

And if x[sup]2[/sup] - 4 = 5, then x can be 3 and -3, right? But -3 is not a root of the original equation.

I’ll let you think about why this method doesn’t work for a while.

[kaylasdad99]

also, if x[sup]2[/sup] - 4 = x + 2, then (x+2)(x - 2) = (x + 2).

Therefore, (x - 2) = 1

and x = 3.

[kaylasdad99]

@ultrafilter

And if x[sup]2[/sup] - 4 = 5, then x can be 3 and -3, right?

No, it can’t, because it also has to fit x + 2 = 5 at the same time (Simultaneous equations). Only 3 does that.

[moriah]

How can x be two different answers?!

Consider this x[sup]2[/sup] = 4

x can be either 2 or -2. When you have a squared variable, you often (though, not always) have two answers.

Now, watch this. Take x[sup]2[/sup] = 4

and subtract four from both sides… x[sup]2[/sup] - 4 = 0

Factor the quadratic… (x+2)(x-2) = 0

Now, we know, that when you have the product of any two numbers equaling zero, then one of those numbers equals zero. And so… either

x+2 = 0

or x-2 = 0

Solve for both. This means x is either 2 or -2.
Peace.

[Thudlow_Boink]

Remember, kaylasdad99, that x = 3/4 is also a solution, which your method doesn’t find.

[ultrafilter]

kaylasdad99, you got lucky with this equation. In general, say you’ve got an equation like this:

1/(x[sup]2[/sup] - a[sup]2[/sup]) + 1/(x - a) = 1/b

By your method, x - a = b, and x[sup]2[/sup] - a[sup]2[/sup] = b. So it follows that x = a + b and x[sup]2[/sup] = a[sup]2[/sup] + b. So (a + b)[sup]2[/sup] = a[sup]2[/sup] + b. Expand to get a[sup]2[/sup] + 2ab + b[sup]2[/sup] = a[sup]2[/sup] + b. Cancel and rearrange, and you get this:

b[sup]2[/sup] + (2a - 1)b = 0

The roots of that are b = 0 and b = 1 - 2a. So with a = 3, you need b = -5, and given the following equation, your method generates the wrong answer:

1/(x[sup]2[/sup] - 9) + 1/(x - 3) = 1/4

[samclem]

@astro

I’ve wondered about this for awhile now, and since this is the place to put these questions -

I really think the SDMB policy on homework questions, and specifically math homework questions is a bit too restrictive.

So, I/we should allow math questions, but perhaps scrutinize other homework questions more closely? Does that mean that other subjects are “soft” and don’t deserve help? Who makes up the list?

A lot of people are probably thinking “Lazy students! Just work harder”, but that’s not the way it is. In getting your head wrapped around abstract math concepts a good example and guide is like gold, and unfortunately a lot of people at the lower end of the math intuitive curve are intimidated in large groups from asking “I don’t get it” questions. It’s abjectly humiliating.

That’s what tutors are for. Or the teacher after class/hours.

Beyond this, I’ve seen a few math questions sneak under the wire here, and the level of guidance offered is truly superlative. It’s head and shoulders above a lot of the classroom examples offered, and the SDMB respondents who offer help don’t seem to mind. Some math snobs might disdain the simple algebra help requests, but many math mavens here are glad to help.

I can’t disagree. Smart people here. That’s why we’re the best board on the net. But, you can overdo a good thing. I think that’s what we’re trying to avoid.

Invariably these “please help me” threads often get shut down with stern mod warnings about not asking the SDMB for help with [thunder crash]“HOMEWORK QUESTIONS”.[/thunder crash]

I though I did a pretty nice job of the latest one, both in the original thread, and in the one asking why I closed the thread. (and, now in the thread about the general policy.)

Why are we so anal about this? We answer questions about goat porn for Gods sake, but lord help you if you’ve got a homework question!

My guess–there aren’t 100 people who will post a goat-porn question to this board(but, hey! I’m always surprised every day I read threads here :eek: ) But there are literally thousands who would post a homework question.

Most people aren’t asking us to write term papers. It’s typically 1:00 AM and they’ve got a stumper they need some help with. Why not offer a helping hand? Limit it to registered members, or maybe set a forum for it, but to ban these questions entirely seems mean spirted, and to some degree, against the basic “Fighting Ignorance” ethos of this board.

Well, you can’t limit it to registered=paid members. We aren’t trying to be a paid tutorial service. I’ll personally try harder to not automatically flush a poster asking for “help” with homework, especially if they’ve done most of it, and just need a boost.

Not having a hard/fast rule makes it up to us as individuals to try to maintain order/limits on what happens on this board. We ain’t perfect.

Thanks for the input.

[kaylasdad99]

@Thudlow Boink

Remember, kaylasdad99, that x = 3/4 is also a solution, which your method doesn’t find.

Just so. I re-checked my work while I waited for my bus this afternoon, and realized that you and ultrafilter are correct. Sorry.