I am having trouble transposing the equation below, I need to make 'v' the subject. My main problem is that I am not sure how to get rid of the division. Any help would be greatly appreciated.

F= u * v / u + v

Many thanks

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- Feb 15th 2013, 05:50 AMjcalowTransposing an equation
I am having trouble transposing the equation below, I need to make 'v' the subject. My main problem is that I am not sure how to get rid of the division. Any help would be greatly appreciated.

F= u * v / u + v

Many thanks - Feb 15th 2013, 06:04 AMPlatoRe: Transposing an equation
- Feb 15th 2013, 06:10 AMebainesRe: Transposing an equation
I assume what you mean is this: F = uv/(u+v). Parentheses are important!

Starting with

$\displaystyle F = \frac {uv}{u+v}$

multiply through by (u+v) to get

$\displaystyle F(u + v) = uv $

Rearrange to get the 'v' terms on the left hand side:

$\displaystyle Fv - uv = -Fu$

$\displaystyle v (F-u) = -Fu $

Divide through by (F-u):

$\displaystyle v = \frac {-Fu}{F-u}$

You can get rid of the minus sign on the right if you want:

$\displaystyle v = \frac {Fu}{u-F} $