algebra

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Solve x-9/x^2-4 < 0 and write interval notation

  • algebra -

    Note:
    x-9/x^2-4 < 0 ≠ (x-9)/(x^2-4) < 0

    I presume it is the latter, and that you have omitted to insert parentheses when interpreting a fraction.

    The best way to visualize the problem is to sketch a graph of the function (of the left-hand-side).

    The numerator is positive for x>9, and negative for x<9.

    The denominator is >0 for |x|>2, and <0 for x<2.

    Note that there is a vertical asymptote at x=2.

    So make a table:
    interval numerator denominator expression
    (-∞,-2) <0 >0 <0
    (-2,2) <0 <0 >0
    (2,9) <0 >0 <0
    (9,+∞) >0 >0 >0

    From the table, it should be relatively easy to find the solution to f(x)<0.


    For reference:
    http://img811.imageshack.us/img811/4262/1291593942.png

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