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           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality 1/(x−9)+1/(x+2) ≥2x/(x^2+x−2) .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality：
        1 / ( x - 9 ) + 1 / ( x + 2 ) ≥2 * x / ( x ^ 2 + x - 2 )         (1)
        From the definition field of divisor
         x - 9 ≠ 0        (2 )
        From the definition field of divisor
         x + 2 ≠ 0        (3 )
        From the definition field of divisor
         x ^ 2 + x - 2 ≠ 0        (4 )

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    From inequality(1)：
         x ≤ -2 或  -7/9 ≤ x ≤ 1 或  x ≥ 9
    From inequality(2)：
         x < 9 或  x ＞ 9
    From inequality(3)：
         x < -2 或  x ＞ -2
    From inequality(4)：
         x < -2 或  -2 < x < 1 或  x ＞ 1

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    From inequalities (1) and (2)
         x ≤ -2 或  -7/9 ≤ x ≤ 1 或  x ＞ 9    (5)
    From inequalities (3) and (5)
         x < -2 或  -7/9 ≤ x ≤ 1 或  x ＞ 9    (6)
    From inequalities (4) and (6)
         x < -2 或  -7/9 ≤ x < 1 或  x ＞ 9    (7)

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    The final solution set is :
         x < -2 或  -7/9 ≤ x < 1 或  x ＞ 9

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