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I'm in need of an algebra refresher course.

  1. May 31, 2008 #1
    I managed to confuse the heck out of myself, so I'll post the impossible conclusion I recently made.


    I don't know why not, but this is impossible and I know it, but it seems to make perfect sense. Keep an eye on the 1 in the denominator and the 8 in the numerator.


    See, it "feels" like it makes perfect sense to "uncancel" an invisible x. However, something doesn't feel right. I then do the following (which then gives me an even more impossible conclusion.)


    I cancel the x in the denomenator in trade for bringing the cubic up stairs down to a square.

    [tex]\frac{2x^2 + 16x}{2x+1}[/tex]

    Subtracting and adding terms in the numerator.

    Now I take 2x and cancel from both 16x and [tex]2x^2[/tex], which yields:

    [tex]{x^2 + 16}[/tex]

    I'm getting a sick feeling in my stomach for not being able to understand what's going wrong here, I've never had trouble with algebra, especially not with something like this. -_-; I think it's high time for a refresher course. Can someone target what I've done wrong here, and maybe point me to a good source to brush up on the basics? Many thanks in advance.

    *I just noticed, after posting, that I made the 2x from 2x+1 vanish all together, instead of leaving a 1, that conclusion should have been [tex]{x^2 + 8}[/tex]; I still don't think that adds up though.
    Last edited: May 31, 2008
  2. jcsd
  3. May 31, 2008 #2


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    How about a refresher course in arithmetic? If you have (5+ 1)/(2+1) can you cancel the "1"s and say that is equal to 5/2? No, of course you can't. Because "canceling" in a fraction really means divide- the opposite of multiplying. When you cancel, you are "undoing" a multiplication. You cannot cancel the "1"s because they are not multiplying the "3" and "2".

    You can cancel the "2"s in 2(3)/(2)(1) to get 3/1= 3 because they are multiplying numbers and so you can "undo" that multiplication.

    Similarly, you cannot cancel an "x" from one term in the denominator with an "x" from one term in the numerator because they are not multiplying the rest of the numerator and denominator.
  4. May 31, 2008 #3


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    Yeah, just like OJ Simpson has never had any trouble with the law.

    Seriously though I do find it hard to believe judging from what you've just posted.That stuff is so far off the mark it's crazy.
  5. May 31, 2008 #4
    Can anyone get that numerator to factor out?

    I tried, but currently to no avail.
  6. May 31, 2008 #5


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    By the rational root theorem the only possible rational roots that the numerator could have are +1, +2, -1 or -2, none of which work so any real roots will be irrational.
  7. May 31, 2008 #6


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    2x+ 1 divides into 4x3+ 2x2+ 8x+ 8 2x2+ 4 times with a remainder of 4 so that fraction cannot be reduced.
  8. May 31, 2008 #7
    I ought to silly slap some of the people in this thread. If I'm "that bad at algebra" I wouldn't be looking for a refresher course, I'd silently go pick up a copy of 'The Idiots Guide to Algebra,' and figure it out myself. That last part was a mistake while converting the problem into [tex] format, I even added an edit there for that one (actually I suppose I should have just overwritten it, instead of adding it down at the bottom.) And no thanks to anyone from here, I already found what I was screwing up. I managed to over look that the numerator is sharing a common denomenator. That doesn't require a refresher course in arithmetic, lucky for me.

    Remember, if something looks too stupid to be true, you're probably not understanding where their confusion is comming from.


    Also, why the hell would I need to lie and say I'm good at algebra if I'm not? This is the internet, it's completely anonymous. Even if I liked this username and wanted to give it a good name, I could just go on an unsecured network on my laptop and make an alt account to ask the question (I know where several are in my friend's appartment complex, it would be pretty damn easy.) No one would ever know it was "kts123" who asked just a stupid question. The only thing so off the mark it's crazy is someone thinking I'd lie about my abilities for no damn reason at all. I could just say "I suck at algebra, help please." In fact, people do it all the time here and get friendly responses.
    Last edited: May 31, 2008
  9. May 31, 2008 #8
    I don't mean to be cruel but...

    Sorry, but not one of the manipulations you made in your entire post is valid, so like you said, you may want to pick up such a book. (Also, the statement "the numerator is sharing a common denominator" doesn't make any sense. There's no denominator is a numerator. I think you meant that the numerator and denominator share a common factor, which is false.)

    Even with your correction, your result is still completely false.

    Sorry >_<
    Last edited: May 31, 2008
  10. May 31, 2008 #9
    And they all shared the same root mistake! I got one piece of information bass ackwards and it ruined the entire solution. You know, another train of thought would be "if he says he's decent at algebra, he's obviously overlooking something that ruined the whole solution."

    Of course being rude is easier than trying to be helpful.
  11. May 31, 2008 #10
    Let me spell this out for you:

    [tex]\frac{2x+1}{x}[/tex] is NOT 3, because [tex]\frac{2x+1}{x}[/tex] = [tex]\frac{2x}{x}[/tex] [tex]+ \frac{1}{x}[/tex]. We can't "cancel the x" because 2x and +1 are sharing it. Whereas [tex]\frac{2x}{x}[/tex] = 2, we CAN cancel the x. That's all I was overlooking, that ONE stupid mistake ruined everything.

    Oh, and of course everything makes perfect sense to me after that one piece of information comes back. [tex]\frac{2x}{x}[/tex] [tex]+ \frac{4x}{x} = \frac{2x+4x}{x} = \frac{x(2+4)}{x} [/tex] Then, finally, cancel the damn x. What I did was pretty damn stupid, I'll admit, but it was a single mistake that screwed it all up.
    Last edited: May 31, 2008
  12. Jun 1, 2008 #11


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    Whoops I originally also had +/- 1/2 and +/- 4 there in that list of candidates for rational roots but somehow I missed them when I cut and pasted. Anyway the conclusion is the same, none of the candidates work so there are no rational roots.

    To kts123. Yes it was basically the same mistake repeated many times. That particular mistake is a fairly major one however. Anyway the thing to remember is that you can only cancel factors. Maybe it would help you to do some revision of factorization and get really clear in your mind exactly what it means for something to be a factor of an expression.
    Last edited: Jun 1, 2008
  13. Jun 1, 2008 #12
    Yes, it's a huge and very embarrassing mistake. I've already reviewed a lot of factorization, luckily it feels as though everything is flooding back extremely rapidly (and clearly.) My problem is over confidence, in the past couple of years I've stopped bothering with simplfying expressions when it's the last step (and since I'm my only supervisor, I can get away with it.) The fruits of being lazy like that obviously just started dropping.
  14. Jun 1, 2008 #13
    I never thought that you were lying.

    Sorry, it's a well known effect of psychology that most people believe that they are good at something unless they know a decent amount about the subject, completely regardless of their ability.

    So you often have people saying that they are good at a subject who are actually really terrible at it. It's not that they are lying about their ability (after all, if they are talking about the subject, everyone who listens can see how bad they are, so there is no reason to try to get away with lying about it). They sincerely believe that they are good at it. Unfortunately, it's also been found that telling a person that he or she is bad at the subject usually does not convince him, and while pointing out flaws will sometimes convince the person that he did not understand a specific point, he will usually still believe that he is good at the subject and just needs to fix that "one point of misunderstanding".

    As an example of this, occasionally on this forum you will find people who are commonly referred to as "crack pots", who post complete nonsense. People inform them that what they have written is in fact nonsense, but no amount of this will usually convince them. Their posts are deleted; they are banned; they are told not to come back, but these things still do not deter them or convince them that they do not know the subject as well as they believe. Fortunately, it's not too common on this forum, but I've seen other forums where the ratio of crack pots to people who have actually studied the subject is about 50-50.

    Once such a person learns more about the subject though and meets people who are good at the subject and can do things that he cannot, then the person usually comes to realize that he was not in fact good at the subject. This has the effect that people who are experts in the field will often times believe that they are at most "above average" because they have met many people who are better than they in specific things. For people suffering from this though, usually just informing them of how well other people in their field are at the subject is enough to convince them of where they stand.


    I did not inform you of this to suggest that you are suffering from this in any way. I only did to explain to you why I (and many other people) will tend to ignore someone's self description of their ability they only say that they are good or bad. (Have you ever been at a gathering and someone has an instrument and someone tries to convince them to play, but they said that they're really terrible it at, and they turn out to actually be really good? Or on the other hand, have you ever been at a similar gathering, and someone tries to show off by playing an instrument, and they turn out to be really terrible? -- both of these seem to be a lot more common than a person accurately describing how good they are)

    Unfortunately, in your case, you said that you were good, and then followed with something full of mistakes. True, it was only a few mistakes repeated many times, but it was a very elementary one. It's common to get such things confused after not doing something for a while though. So if that really was the only thing that you were confused about, then good; I'm glad that you could find help on this board.
  15. Jun 1, 2008 #14
    I never said I was good at algebra, I said I've never had any trouble with it! I'd learn a new concept, it'd make sense, I'd apply it well on my tests and get good grades -- end of story. I'm not top tier, but I'm not one of those dimwits who says "math lost me when it started using letters." That's all I was saying, damnit.

    In fact most people don't have trouble with it, so it wouldn't surprise me if I am in fact well below average when it comes to algebra, but I just wasn't so bad that I flunked out. Especially if this mistake is as moronic as everyone here is acting -- I actually needed HELP to figure this one out? That doesn't say much for my abilities.
    Last edited: Jun 1, 2008
  16. Jun 1, 2008 #15


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    kts123, advice about a refresher course on Algebra is that you could either study on your own from either an Intermediate Algebra book or a College Algebra book. If you really believe that you need a teacher-based course instead, then use a community college; you may also have the opportunity to study the course from that institution in a self-paced/semi-independant manner if the school offers this option.
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