# Thread: Transposition problem

1. ## Transposition problem

Hello everyone.

I have just started a new college course which involves an analyticalmethods module. We have just started transposition and have been given thefollowing:

F=uv/u+v

Transpose to find v

I have racked by brain for a bit and came up with..

v=f/u-u

Is this right? not sure if I have it right, can anyone help out?

2. ## Re: Transposition problem

It would be more clear if you used brackets.
Is it:
$F=\frac{u\cdot v}{u+v}$ or $F=\frac{u\cdot v}{u}+v$
?

3. ## Re: Transposition problem

Originally Posted by wysiwyg
Hello everyone.

I have just started a new college course which involves an analyticalmethods module. We have just started transposition and have been given thefollowing:

F=uv/u+v
I assume you mean F= uv/(u+v), not F= (uv/u)+ v since the latter would be just 2v.

Transpose to find v

I have racked by brain for a bit and came up with..

v=f/u-u

Is this right? not sure if I have it right, can anyone help out?

No, that is not correct. If you multiply both sides by u+ v, you get F(u+ v)= uF+ vF= uv.
Then uF= uv- vF= v(u- F). Can you finish it?

4. ## Re: Transposition problem

Originally Posted by Siron
It would be more clear if you used brackets.
Is it:
$F=\frac{u\cdot v}{u+v}$ or $F=\frac{u\cdot v}{u}+v$
?
Apologies, I should have used brackets.

Its the first one...

5. ## Re: Transposition problem

No problem.
HallsofIvy has given you a hint. Can you continue? ...

6. ## Re: Transposition problem

Thanks guys, just trying to work through it now...

Bit confused with the two sets of equal signs tho i.e F(u+ v)= uF+ vF= uv

Unless I am reading it wrong...

7. ## Re: Transposition problem

$F=\frac{uv}{u+v}$
Step 1: Multiply both sides with $u+v$ (like HallsofIvy said):
$F(u+v)=uv$
Step 2: Work the brackets out:
$Fu+Fv=uv \Leftrightarrow Fu=uv-Fv \Leftrightarrow Fu=v(u-F)\Leftrightarrow v=...$

Is this clear? ...

8. ## Re: Transposition problem

Originally Posted by Siron
$F=\frac{uv}{u+v}$
Step 1: Multiply both sides with $u+v$ (like HallsofIvy said):
$F(u+v)=uv$
Step 2: Work the brackets out:
$Fu+Fv=uv \Leftrightarrow Fu=uv-Fv \Leftrightarrow Fu=v(u-F)\Leftrightarrow v=...$

Is this clear? ...
Yes it is, thank you...

Is it: v=Fu/(u-F) ?

Correct!

10. ## Re: Transposition problem

Thank you for your help (Siron/HallsofIvy), much appreciated.

11. ## Re: Transposition problem

You're welcome!