# Transposing an equation

• Feb 15th 2013, 05:50 AM
jcalow
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
• Feb 15th 2013, 06:04 AM
Plato
Re: Transposing an equation
Quote:

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

$\displaystyle F(u+v)=u\cdot v$.
• Feb 15th 2013, 06:10 AM
ebaines
Re: Transposing an equation
Quote:

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

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

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:

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