A rather simple (maybe stupid) math question.

It’s a simple high school math question that I need help with for homework. Here it is:

If 1/u + 1/v = 2/f, then [1/(f-u)] + [1/(f-v)] = …

You don’t have to give me the answer necessarily, but it’d be nice to give me a point in the right direction. Thanks.

And I’m supposed to be the smart one in the family…

Hmm… Should I help with a homework problem? Ok. This’ll probably be closed very soon, but…

When adding two fractions you must make the denominators the same. When they are, you just add the numerators. And since 1 + 1 = 2…

[1/(f-u)] + [1/(f-v)] = [1/(f-u)] + [1/(f-v)], and they can’t claim that’s wrong. However, I suspect that you’re being asked to evaluate the expression in terms of u and v. This is a pretty simple process:

  1. Solve the first equation for f.

  2. Substitute the value of f in the second expression.

  3. Simplify.

This sort of procedure comes in quite handy in high-school algebra.

I dislike it when people are snarky about homework problems. If you have never sat in your bedroom at the verge of tears because this math problem has been pissing you off for the last hour and you have tried everything you can think of and you don’t know what to do, then good for you. Some of us have.

Are you sure it’s not [u/(f-u)] + [v/(f-v)] = ?

Actually, for one set of values u, v, and f, the answer would exactly fit the equation [1/(f-u)] + [1/(f-v)] = … (and the answer is fairly straightforward). I have not tried solving it for alternative values of u, v, and f, yet.

Agree (though I don’t see much snarkiness around here, just caution). Board rule sez: “Please do not ask other members to do your homework or provide input for your article, paper, or other off-board project.” However, it does not say that you can’t ask for help. Pointing someone in the right direction is not doing their homework for them.

Well, I have to get snarky here. I have to say that if you’ve sat in your bedroom for an hour then you haven’t tried everything you can think of. If you’ve got homework, at least 10-20 people you know have the same homework and you can beat feet over to form a study group, or pick up the phone. There’s a lot of distance that can be covered between beating your head into a textbook and dropping a message to an Internet board full of wackos.

I think Ultrafilter has the best advice here, which provides a method without doing the work for you.

I may be hasty, but it appears that any solution of u, v, and f in the first equation produces the same result in the second equation–and it remains pretty straightforward.

Unfortunately, I’m using the gazinta method rather than legitimate math, so I cannot provide a proof. However, I would agree with ultrafilter that solving for the variables will provide the answer needed.

HEY! We resemble that remark.

The second bit doesn’t look like an equation to me. I think this is the sort of problem where the student is asked to simplify an expression subject to the constraints given by a set of equations.

You think that’s snarky? For someone who’s asking someone else to do their work for them? Hell, if I weren’t working on getting a preprint out I’d come up with an astoundingly complicated (but thorough and correct) answer for him to copy onto his homework and get called out on it.

No one’s asking anyone to do their work for them:

Learning methodology is part of the work. To say “solve for one variable and put it into the second equation” is just restating the problem. To go any farther gives it away. It is the student’s responsibility to (a) read the book or (b) approach the instructor.

Take away the Internet from this equation - say the OPs father had a bunch of friends over for dinner, and she knew some of them were pretty good with math. Would it be wrong of her to call some over and ask them to help her understand how to tackle the problem? Approaching the teacher isn’t always a feasible solution - especially with high school teachers who have 100 students a day, and very little time to dedicate to one particular student.

Yes, I’d say it would be wrong, for the exact same reasons. If the student doesn’t know the answer to a problem, has not learned it from the instructor’s lessons, and cannot learn it from the book, then the student needs to get it wrong. If there is no penalty, the student has no reason to put in the extra effort to master the concept. Further, the instructor will have no idea what concepts the student (and other students) are really learning, and will be unable to modify the lesson plans to compensate.

As for it being infeasible to approach the instructor, this is simply blame-shifting. “I can’t ask the person who’s supposed to be presenting this material because he’s too busy, thus it’s not my fault.” Instructors, even at the high school level, are so used to disinterested and disengaged students that I dare say the OP’s teacher would faint with joy to have a student actually admit they don’t know everything and ask for help. I have never found a single one who was unwilling to assist a student who has the self-awareness to recognize his limitations and ask for help.

I don’t want to hijack this thread any farther than we have already, but if you’ve never met a teacher who was unable to give one-on-one attention to students who needed help because they were overworked, or for any other reason, you’ve been very fortunate.

The point is to learn - it doesn’t matter who you learn it from. Just because she learns to understand it from the Straight Dope or her parents or a tutor or some guy down the street - the point is to learn it, understand it, and use it. Saying she should only learn it from the teacher and the book is shortsighted and way too optimistic for the educational system I’ve been exposed to.

Where did I say it had to be one-on-one attention? The teacher can quickly remind the student which is the relevant section, which takes all of ten seconds. The teacher can realize that that particular subject is not sticking and can review it more thoroughly in class. And yes, the teacher can work one-on-one with the student, but can do so at another time than when approached.

There are further problems with homework here, which show that it does matter. The teacher may have a particular method in mind that we (obviously) don’t know. The question may be transcribed incorrectly. In fact, given the format of the question in the OP I’m certain that something has been omitted. The very nature of the communication makes it impossible to impart the underlying concept. If the student had a qualified tutor, he would see the context in which the problem is being presented, break out similar problems, and attack the comprehension rather than the specific problem.

Finally, I have to say again: the student needs to be incorrect on the problems he doesn’t understand. Giving the SDMB as a resource removes the entire point of homework for the students who avail themselves of it.

Mathochist you’ve got to be kidding.

In any case what’s the answer to the damn problem? I haven’t done this kind of stuff in many years but when I solve for f, u and v, and plug them into the second expression I get a monster. So what are you really suppose to do? What’s the secret here?

Hopefully since the kid is now in school and his homework should have been done by now, can someone tell ME the answer? Please? :slight_smile: I’ve been playing with this for about half an hour and the only thing that makes sense to me given the OP is that u=v=f, which would make the second equation undefined since each denominator would then equal 0.

Provided that u is not equal to v, then the answer is (perhaps surpisingly) also 2/f.

Might I just add that either there was a transcription problem, the OP’s teacher/book is defining “f” in a very different way than the usual, or the problem is not on what it very much looks like it’s on. Would I be correct in surmising that this problem started life as an optics question?