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Math Help - cross multiply

  1. #1
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    Feb 2008
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    cross multiply

    Solve the equations

    x-1/3 = x+5/x-1

    x-1/x+2 = 3/x
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  2. #2
    Super Member

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    Hello, Belanova!

    You have the equations and you have the directions.
    Exactly where is your difficulty?


    \frac{x-1}{3} \;=\;\frac{x+5}{x-1}

    We have: . \frac{x-1}{3}\;=\;\frac{x+5}{x-1}

    Cross-multiply: . \frac{x-1}{3}\!\!\begin{array}{cc} _{\nwarrow} \\ ^{\nearrow}\end{array}\!\!\!\!\begin{array}{c} _{\nearrow} \\ ^{\nwarrow}\end{array}\!\!\frac{x+5}{x-1} \quad\Rightarrow\quad (x-1)(x-1) \:=\:3(x+5)

    . . x^2-2x+1 \:=\:3x+15x \quad\Rightarrow\quad x^2-5x-14\:=\:0

    . . (x+2)(x-7)\:=\:0\quad\Rightarrow\quad\boxed{ x \;=\;-2,\:7}

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