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Math Help - Transposition problem

  1. #1
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    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?

    Thanks in advance.
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  2. #2
    MHF Contributor Siron's Avatar
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    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
    ?
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  3. #3
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    Re: Transposition problem

    Quote Originally Posted by wysiwyg View Post
    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?

    Thanks in advance.
    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?
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  4. #4
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    Re: Transposition problem

    Quote Originally Posted by Siron View Post
    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...
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  5. #5
    MHF Contributor Siron's Avatar
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    Re: Transposition problem

    No problem.
    HallsofIvy has given you a hint. Can you continue? ...
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  6. #6
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    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...
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  7. #7
    MHF Contributor Siron's Avatar
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    Re: Transposition problem

    If we start with:
    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? ...
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  8. #8
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    Re: Transposition problem

    Quote Originally Posted by Siron View Post
    If we start with:
    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) ?
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  9. #9
    MHF Contributor Siron's Avatar
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    Re: Transposition problem

    Correct!
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  10. #10
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    Re: Transposition problem

    Thank you for your help (Siron/HallsofIvy), much appreciated.
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  11. #11
    MHF Contributor Siron's Avatar
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    Re: Transposition problem

    You're welcome!
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