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Math Help - Turning a fraction into a quadratic

  1. #1
    Junior Member
    Joined
    Nov 2008
    Posts
    25

    Turning a fraction into a quadratic

    Hi,

    I'm trying to work out how a question was solved from an example in a book.

    x(squared)
    ------------------- = 6.25
    6 - 5x + x(squared)

    goes to...

    5.25x(squared) - 31.25x + 37.5 = 0

    I don't understand how this was done.

    any ideas?
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  2. #2
    Member
    Joined
    Dec 2008
    From
    Auckland, New Zealand
    Posts
    189
    They have cross multiplied to get the answer.

     \frac{x^2}{6 - 5x + x^2} = 6.25

    \Rightarrow x^2 = 6.25(6 - 5x + x^2)   (cross multiply)

    \Rightarrow x^2 = 37.5 - 31.25x + 6.25x^2  (expanding)

    \Rightarrow 5.25x^2 - 31.25x + 37.5 = 0  (collect terms on one side)
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