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Math Help - Given (a+b)(c+d) = ab+ac+bc+bd, How to express (a+b)÷(c+d) OR

  1. #1
    Newbie wideEyedPupil's Avatar
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    Given (a+b)(c+d) = ab+ac+bc+bd, How to express (a+b)÷(c+d) OR

    Problem: Generating an expression that removes the parentheses using first principles.

    Given (a+b)(c+d) = ab+ac+bc+bd,

    Can we say: (a+b)÷(c+d) = a/c+a/d+b/c+b/d is True? (no we can't if we use test data!)

    What I really want is to express R, so far I know R = (360 over W) - 10 - (R.(T -75W) over W)
    So I'm trying to isolate for R on LHS only.

    Workings:
    If a=b=1 and c=d=2 then
    For (a+b)(c+d),
    ≍ (1+1)÷(2+2)
    ≍ 2÷4 = 1/2
    For a/c+a/d+b/c+b/d,
    ≍ 1/2 + 1/2 + 1/2 + 1/2 = 2 So no it's not true, but invert 2 and it's 1/2 are we close,
    can we say:
    (a+b)(c+d) = _________1_________
    a/c+a/d+b/c+b/d

    Where a=1, b=4, c=2, d=8
    Testing (a+b)(c+d) = (1+4)(2+8)
    =(5)(10) =50
    Testing _________1_________ = _________1_________
    a/c+a/d+b/c+b/d 1/2+1/8+4/2+4/8
    = _________1__________
    4/8+1/8+16/8+4/8

    = ___1___
    25/8
    =8/25 ≠ 50 So no that's not it!

    Please help me. The actual equation I'm trying to simply for programming purposes is:
    R = (360 over W) - 10 - (R.(T -75W) over W)

    I need to express the equation isolating R on one side of equation only.
    Last edited by wideEyedPupil; December 20th 2010 at 12:01 AM. Reason: End goal at top of post
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  2. #2
    Senior Member BAdhi's Avatar
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    see below
    Last edited by BAdhi; December 20th 2010 at 12:47 AM. Reason: misprinted
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  3. #3
    Senior Member BAdhi's Avatar
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    you have given counter examples
    so it's not true

    is this your equation?
    R=\frac{360}{W}-10-\frac{R(T-75W)}{W}

    then
    R[\frac{T-75W}{W}+1]=\frac{360}{W}-10

    R[\frac{T-74W}{W}]=\frac{360-10W}{W}

    R=\frac{360-10W}{T-74W}
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  4. #4
    Newbie wideEyedPupil's Avatar
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    Cheers

    Thanks BAdhi

    This: R[\frac{T-75W}{W}+1] is the bit I didn't get through… Haven't studied/used much maths for 2 decades, cheers!

    Any ideas about a general way to expand \frac{a+b}{c+d}<br />
out of interest? Or is that a pointless question, does one just multiple both sides of an equation by (c+d)?
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  5. #5
    Senior Member BAdhi's Avatar
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    add R\frac{T-75W}{W} to both sides, then take R out

    can you elaborate the idea of \frac{a+b}{c+d}. Because i cannot find anything that is related to it in this equation ?
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  6. #6
    Newbie wideEyedPupil's Avatar
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    No, no I got it the first time, I just meant I couldn't make that leap before you reply to my original post. Cheers. I actually found a different way of expressing my problem and don't need to resolve that term now so I'm going to leave it. I posted on Dr Math before here, kinda by mistake thinking it was this forum, and someone there produced a series that equates to that term.

    His reply is follows:
    Hello,

    (a+b)/(c+d) can certainly be written a/(c+d) + b/(c+d)

    If you do a long division of (c+d) into a you get

    a/c - ad/c^2 - ad^2/c^3 - ad^3/c^4 - ...

    There is a definite pattern here. I don't know whether or not this
    will lead to anything helpful.


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  7. #7
    MHF Contributor
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    What expression are tying to solve? You have 3 expressions in your original post.
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  8. #8
    Newbie wideEyedPupil's Avatar
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    Oh they were different bits of a larger set of equation that has something like 10 variables. Sorry, I was jumping around trying to find ways to express the screen co-ordinates of a visualising bit of software for an (old) exercise program called 5BX. (5BX wikipedia).

    If you are interested I can email you the documentation and code but it's in a visual programming language called Quartz Composer which is Mac OS X only (free with Apples Developer Tools that ships with every mac). It's just the running section that was proving tricky because the number of steps get's divided by 75 after which 10 star jumps are performed and usually there is and odd number of steps left over after a series of running and jumping blocks. Calculating the time spent on each phase involved simultaeous equations in time equations and transposing those to dimensional values. QC is quite handy at expressing all the interrelated equations as it's a graph of patches that gets evaluated with lazy evaluation each frame (functional language).

    Movie of output (10Mb h264):
    http://dl.dropbox.com/u/1585739/5BX%20math.mov
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