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Math Help - Ratio-inequation

  1. #1
    Super Member dhiab's Avatar
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    Ratio-inequation

    Solve in R :
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  2. #2
    MHF Contributor red_dog's Avatar
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    The inequality is equivalent to \frac{x^2-4x-4}{x^2+4x-4}\geq 0

    <br />
\begin{array}{c | c c c c c c c c c c c}<br />
x & -\infty & -2-2\sqrt{2} & 2-2\sqrt{2} & -2+2\sqrt{2} & 2+2\sqrt{2} & \infty\\\hline\<br />
  x^2-4x-4 & + & + & +0- & - & -0+ & +\\\hline<br />
x^2-4x-4 & + & +0- & - & -0+ & + & +\\\hline<br />
E(x) & + & +|- & -0+ & +|- & -0+ & +\\<br />
\end{array}<br />

    Then x\in(-\infty,-2-2\sqrt{2})\cup[2-2\sqrt{2},-2+2\sqrt{2})\cup[2+2\sqrt{2},\infty)
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