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Math Help - Division To Subtraction Equivalence

  1. #1
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    Division To Subtraction Equivalence

    Hey everyone, I've just joined the forum. it's great to be here. Ok I need some help with a problem I've been trying to solve.

    Here it is. Given the following expression:

    R / (D-i) = T

    Where D is constant and R and T are dependent variables, and (i) is a discrete increasing interval which begins at 0 and approaches D.

    I would like to convert this expression into a subtraction rather than a division (For convenience purposes).

    When rearranging it we get:

    R = T(D-i)

    This looks elegant but I need T to be the subject of the formula while avoiding divisions and have so far not found a way. My gut is telling me that this requires a series approximation (E.g Maclauren Series) but I am not certain how to go about this.

    Ideally I would end up with an expression similar to the following:

    T = A - B - C ....... - N

    I would really appreciate any help you can offer me, I have a feeling this is a lot simpler than it looks and I've missed something!

    Thanks
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Division To Subtraction Equivalence

    If T is the subject then starting with:

    T = \frac { R}{D-i}

    you can apply long division to the right hand side, and what you get is:

    T = \frac R D + \frac {Ri}{D^2} + \frac {Ri^2}{D^3} + \frac {Ri^3}{D^4} + ...

    Hope this helps.
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  3. #3
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    Re: Division To Subtraction Equivalence

    That's amazing help friend. Thank you very much!

    Ben
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  4. #4
    MHF Contributor ebaines's Avatar
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    Re: Division To Subtraction Equivalence

    You're welcome! I would add that this series converges as long as -D< i< D, which I believe is OK for what you're trying to do.
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