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Math

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I need help on how to solve this type of problem please.

29.)Solve the inequality and express the solution in terms of intervals whenever possible.

1/(x-2) ≥ 3/(x+1)


THE ANSWER IS: ( -∞,-1 ) U ( 2,(7/2) ]

  • Math -

    1/(x-2) - 3/(x+1) ≥ 0

    So we have critical values at x = -1 and x = 2

    test for any value x < -1, e.g. x = 10
    is 1/-12 ≥ 3/-9 ? YES
    test for any value between -1 and 2, say x = 1
    is 1/-1 ≥ 3/2 ? NO
    test for any value x > 2, say x = 5
    is 1/3 > 3/6 ? YES

    so solution is
    x < -1 OR x > 7/2

    suggestion:
    enter 1/(x-2) - 3/(x+1)
    into "first graph" of
    http://rechneronline.de/function-graphs/

    to see where the graph is above the x-axis.

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