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Simple algebra, derivations, integrations. Desperate need of help

  1. Dec 20, 2004 #1
    Simple algebra, derivations, integrations. Desperate need of help :)

    Hi!
    This is my first post here (and it's not a very funny one). :)

    It's been a long time since I took any math, and I'm getting more and more confused. Need some help!

    a'*m' = b'*m
    a*m' = b*m

    b-b'=(a-a')*(m/m')
    (a-a')+(b-b')=(a-a')*(?)

    What's supposed to fit where the question mark stands?

    More stupid questions to come. :cry:
     
  2. jcsd
  3. Dec 20, 2004 #2
    Let us denote the questionmark with "x", so that we have:

    (a - a') + (b - b') = (a - a') * x.

    Divide both sides by (a - a'):

    x = ((a - a') + (b - b')) / (a - a') = 1 + (b - b') / (a - a') ... (1)

    But you knew that (b - b') = (a - a')(m/m'), i.e that (b - b')/(a - a') = (m/m'), so

    x = 1 + m/m' ... (2)

    Both (1) and (2) are possible answers.
     
  4. Dec 20, 2004 #3

    HallsofIvy

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    You have b-b'=(a-a')*(m/m')

    You go from b- b' to a-a'+ b- b' by adding a- a', of course. Doing that on both sides, you get a+ a'+ b- b'= a+ a'+ (a-a')(m/m')= (a-a')(1)+ (a-a')(m/m').

    Now seeing that "(a- a')" in both parts on the right, you can factor it out:

    a+ a'+ b- b'= (a-a')(1+ (m/m')).
     
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