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Math Help - Factoring

  1. #1
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    Factoring

    3x - \frac{7}{x} = 5

    I dont like fractions.-_-"
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  2. #2
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    Quote Originally Posted by hydride View Post
    3x - \frac{7}{x} = 5

    I dont like fractions.-_-"
    3x - \frac{7}{x} = 5

    x\left(3x - \frac{7}{x}\right) = 5x

    3x^2 - 7 = 5x

    3x^2 - 5x - 7 = 0

    3\left(x^2 - \frac{5}{3} - \frac{7}{3}\right) = 0

    3\left[x^2 - \frac{5}{3} + \left(-\frac{5}{6}\right)^2 - \left(-\frac{5}{6}\right)^2 - \frac{7}{3}\right] = 0

    3\left[\left(x - \frac{5}{6}\right)^2 - \frac{25}{36} - \frac{84}{36} \right] = 0

    3\left[\left(x - \frac{5}{6}\right)^2 - \frac{109}{36}\right] = 0

    3\left[\left(x - \frac{5}{6}\right)^2 - \left(\frac{\sqrt{109}}{6}\right)^2\right] = 0

    3\left(x - \frac{5}{6} + \frac{\sqrt{109}}{6}\right)\left(x - \frac{5}{6} - \frac{\sqrt{109}}{6}\right) = 0
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