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Thread: Make x the subject

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    4

    Make x the subject

    Hi

    Where am I going wrong in trying to rearrange this:

    $\displaystyle
    \frac{x+a}{x+b} = c
    $

    $\displaystyle
    x+a = c(x+b)
    $

    $\displaystyle
    \frac{x+a}{c} = x+b
    $

    $\displaystyle
    \frac{x+a}{c}-b = x
    $

    $\displaystyle
    x+a - cb = xc
    $

    $\displaystyle
    a - cb = xc - x
    $

    $\displaystyle
    \frac{a-cb}{c} = x - x
    $

    Thanks
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  2. #2
    Super Member Failure's Avatar
    Joined
    Jul 2009
    From
    Zürich
    Posts
    555
    Quote Originally Posted by preid View Post
    Hi

    Where am I going wrong in trying to rearrange this:

    $\displaystyle
    \frac{x+a}{x+b} = c
    $

    $\displaystyle
    x+a = c(x+b)
    $

    $\displaystyle
    \frac{x+a}{c} = x+b
    $

    $\displaystyle
    \frac{x+a}{c}-b = x
    $

    $\displaystyle
    x+a - cb = xc
    $

    $\displaystyle
    a - cb = xc - x
    $
    Ok thus far, although a bit longwinded. But now factor out x on the right side first:

    $\displaystyle a-cb=x(c-1)$
    and divide both sides by $\displaystyle c-1$ to get:

    $\displaystyle \frac{a-cb}{c-1}=x$
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