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Math Help - Inequation

  1. #1
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    Inequation

    I don't know what was done to get the line starting with i.e.
    Attached Thumbnails Attached Thumbnails Inequation-scan-1.jpg  
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  2. #2
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    (x-1)(3-x)^2 > x(3-x)(x-1)^2

    (x-1)(3-x)^2 - x(3-x)(x-1)^2 > 0

    pull out the common factors ...

    (x-1)(3-x)[(3-x) - x(x-1)] > 0
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  3. #3
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    I don't know how the next line was made.
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  4. #4
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    For any numbers a and b, a^2- b^2= (a- b)(a+ b)

    3= (\sqrt{3})^2 so 3- x^2= (\sqrt{3})^2- x^2= (\sqrt{3}- x)(\sqrt{3}+ x)

    I think that is what you are refering to but, of course, I can't be certain what you mean by "the next line".
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  5. #5
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    I understand that. I don't understand how the second line becomes the 3rd line.
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  6. #6
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    (x-1)(3-x)^2 > x(3-x)(x-1)^2

    (x-1)(3-x)^2 - x(3-x)(x-1)^2 > 0

    pull out the common factors ...

    (x-1)(3-x)[(3-x) \textcolor{red}{- x(x-1)}] > 0

    distribute ...

    (x-1)(3-x)[3-x \textcolor{red}{- x^2 + x}] > 0

    combine like terms ...

    (x-1)(3-x)(3-x^2) > 0
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  7. #7
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    Thanks. I was misreading the equation.
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