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Thread: Transposing an equation

  1. #1
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    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
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  2. #2
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    Re: Transposing an equation

    Quote Originally Posted by jcalow View Post
    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
    $\displaystyle F(u+v)=u\cdot v$.
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  3. #3
    MHF Contributor ebaines's Avatar
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    Re: Transposing an equation

    Quote Originally Posted by jcalow View Post
    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} $
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