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9 October, 02:54

Solve for x: 4 over x plus 4 over quantity x squared minus 9 equals 3 over quantity x minus 3?

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  1. 9 October, 03:23
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    4/x + 4 / (x²-9) = 3 / (x - 3)

    4 / x + 4 / [ (x - 3) (x + 3) ] = 3 / (x - 3) / * x (x - 3) (x + 3)

    Restrictions : x ≠ 0, x ≠ - 3, x ≠ 3;

    4 (x + 3) (x - 3) + 4 x = 3 x (x + 3)

    4 (x² - 9) + 4 x = 3 x² + 9 x

    4 x² - 36 + 4 x - 3 x² - 9 x = 0

    x² - 5 x - 36 = 0

    x² - 9 x + 4 x - 36 = 0

    x (x - 9) + 4 (x - 9) = 0

    (x - 9) (x + 4) = 0

    x - 9 = 0, or : x + 4 = 0

    Answer:

    x = 9, x = - 4
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