# Math Help - Transposition of Formulae

1. ## Transposition of Formulae

Hi there, I am fairly comfortable with tranposing formulae, however I have been unable to re-arrange this formulae with respect to x. I am having trouble as there are two x components in the formulae.

Any help with this greatly appreciated...

Transpose to make x the subject of the equation:

y = (r + x)
(1 - rx)

Thanks again for any help with this.

Mike

2. Originally Posted by mikewhant
Hi there, I am fairly comfortable with tranposing formulae, however I have been unable to re-arrange this formulae with respect to x. I am having trouble as there are two x components in the formulae.

Any help with this greatly appreciated...

Transpose to make x the subject of the equation:

y = (r + x)
(1 - rx)

Thanks again for any help with this.

Mike
$y=\frac{r+x}{1-rx}$
cross multiply and
try to keep terms contains x in LHS and other terms in RHS

if stuck look spoiler
Spoiler:

$(1-rx)y=(r+x) \quad \Rightarrow \quad y-rxy=r+x$
$\Rightarrow y=r+x+rxy \quad \Rightarrow \quad y=r+x(1+ry)$
$\Rightarrow x(1+ry)= y-r \quad \Rightarrow \quad \boxed { x= \frac{y-r}{1+ry} }$

3. ## Thanks alot!

Thanks alot for that, i understand it alot better now. Just one further point though, in the second line of your workings in the spoiler, I'm not too sure how it was factorised to remove the second x.

$(1-rx)y=(r+x) \quad \Rightarrow \quad y-rxy=r+x$
$\Rightarrow y=r+x+rxy \quad \Rightarrow \quad y=r+x(1+ry)$
$\Rightarrow x(1+ry)= y-r \quad \Rightarrow \quad \boxed { x= \frac{y-r}{1+ry} }$
[/spoiler][/quote]

4. Originally Posted by mikewhant
Thanks alot for that, i understand it alot better now. Just one further point though, in the second line of your workings in the spoiler, I'm not too sure how it was factorised to remove the second x.

.....

$\Rightarrow y=r+ x+rxy \quad \Rightarrow \quad y=r+x(1+ry)$
take common x
$\Rightarrow y=r+{ \color{blue}x}+r { \color{blue} x}y \quad \Rightarrow \quad y=r+x(1+ry)$

5. Excellent, thank you very much for your time and help.

Cheers

Mike