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Math Help - Transposition of Formulae

  1. #1
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    Exclamation 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
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  2. #2
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    Quote Originally Posted by mikewhant View Post
    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} }
    Last edited by ramiee2010; October 25th 2009 at 09:33 AM. Reason: typo error
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  3. #3
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    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.

    Thanks again for your help.

     (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]
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  4. #4
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    Quote Originally Posted by mikewhant View Post
    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)
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  5. #5
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    Excellent, thank you very much for your time and help.

    Cheers

    Mike
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