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Math Help - Algebraic Ratio

  1. #1
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    Algebraic Ratio

    Hey, could someone please solve this (go through each step if possible):

    =(a/b-c/b)*(a-b/2(a/b-c/b))

    The answer is apparently, (a^2/2b)-(c^2/2b), but I cant work it out

    Thanks
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  2. #2
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    Re: Algebraic Ratio

    Quote Originally Posted by Albatrossie View Post
    Hey, could someone please solve this (go through each step if possible):
    =(a/b-c/b)*(a-b/2(a/b-c/b))
    The answer is apparently, (a^2/2b)-(c^2/2b), but I cant work it out
    That answer is correct; better shown as: (a^2 - c^2) / (2b)

    Your expression is somewhat ambiguous (even if correctly shown); this is clearer:
    (a/b - c/b) * [a - b(a/b - c/b) / 2]

    Try this way:
    x = (a/b - c/b) ; so expression becomes:

    x * [(a - bx) / 2]

    Continue...then substitute back in...OK?
    Thanks from Albatrossie
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  3. #3
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    Re: Algebraic Ratio

    Ah yes that does make it simpler.

    But I think where I'm having trouble is simplifying after performing certain steps

    For example (working within the second term), (a/b - c/b) = [(ab - cb) / b^2] = [(a - c )/ b], correct?

    Then multiplying this by b = [(ba - bc)/b]?
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  4. #4
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    Re: Algebraic Ratio

    Quote Originally Posted by Albatrossie View Post
    Ah yes that does make it simpler.
    But I think where I'm having trouble is simplifying after performing certain steps
    For example (working within the second term), (a/b - c/b) = [(ab - cb) / b^2] = [(a - c )/ b], correct?
    Then multiplying this by b = [(ba - bc)/b]?
    Relax man!
    b * [(a - c )/ b] = a - c ; over and out!
    Thanks from Albatrossie
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  5. #5
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    Re: Algebraic Ratio

    Woops, my bad

    So then, the second term end up = -c/2?
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  6. #6
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    Re: Algebraic Ratio

    No.
    a - (a-c) / 2
    = (2a - (a-c)) / 2
    = (2a - a + c) / 2
    = (a + c) / 2

    And the 1st term: (a - c) / b

    Since (a + c)(a - c) = a^2 - c^2, then ?????????????
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  7. #7
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    Re: Algebraic Ratio

    Where does the 2a come from??
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  8. #8
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    Re: Algebraic Ratio

    RULE: a + b/c = (ac + b) / c
    Thanks from Albatrossie
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  9. #9
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    Re: Algebraic Ratio

    Thanks for the help! Took some time but got there in the end
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  10. #10
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    Re: Algebraic Ratio

    What are the steps involved in solving for b is this:

    a + ab = 2b
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  11. #11
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    Re: Algebraic Ratio

    Quote Originally Posted by Albatrossie View Post
    What are the steps involved in solving for b is this:
    a + ab = 2b
    Get the b terms together:
    2b - ab = a
    Factor:
    b(2 - a) = a
    Isolate b:
    b = a / (2 - a)

    Do some learning on your own:
    Introduction to Algebra
    Last edited by Wilmer; April 15th 2012 at 02:29 AM.
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