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
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} $