# Math Help - Transposing an equation

1. ## Transposing 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

2. ## Re: Transposing an equation

Originally Posted by jcalow
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
$F(u+v)=u\cdot v$.

3. ## Re: Transposing an equation

Originally Posted by jcalow
F= u * v / u + v
I assume what you mean is this: F = uv/(u+v). Parentheses are important!

Starting with

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

multiply through by (u+v) to get

$F(u + v) = uv$

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

$Fv - uv = -Fu$

$v (F-u) = -Fu$

Divide through by (F-u):

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

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

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