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

Re: Division To Subtraction Equivalence

If T is the subject then starting with:

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

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

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

Hope this helps.

Re: Division To Subtraction Equivalence

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

Ben

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.