Overview: 1 questions will be solved this time.Among them
           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality ((x-1)lnx/(x+1)^2)-((lnx+1)/(x+1))+1/(x(x+1)) >0 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality：
         ( ( x - 1 ) * ln x / ( x + 1 ) ^ 2 ) - ( ( ln x + 1 ) / ( x + 1 ) ) + 1 / ( x * ( x + 1 ) ) >0         (1)
        From the definition field of ln
        x > 0        (2 )
        From the definition field of divisor
         x + 1 ≠ 0        (3 )
        From the definition field of ln
        x > 0        (4 )
        From the definition field of divisor
         x + 1 ≠ 0        (5 )
        From the definition field of divisor
         x * ( x + 1 ) ≠ 0        (6 )

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    From inequality(1)：
         x < 1
    From inequality(2)：
         x ＞ 0
    From inequality(3)：
         x < -1 或  x ＞ -1
    From inequality(4)：
         x ＞ 0
    From inequality(5)：
         x < -1 或  x ＞ -1
    From inequality(6)：
         x < -1 或  -1 < x < 0 或  x ＞ 0

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    From inequalities (1) and (2)
         0 < x < 1     (7)
    From inequalities (3) and (7)
         0 < x < 1     (8)
    From inequalities (4) and (8)
         0 < x < 1     (9)
    From inequalities (5) and (9)
         0 < x < 1     (10)
    From inequalities (6) and (10)
         0 < x < 1     (11)

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    The final solution set is :
         0 < x < 1

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