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Assignment:Find the solution set of inequality ((ln(1+1/x))^-2)*1/(x*(1+x)) >0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( ( ln ( 1 + 1 / x ) ) ^ -2 ) * 1 / ( x * ( 1 + x ) ) >0 (1)
From the definition field of divisor
x ≠ 0 (2 )
From the definition field of ln
1 + 1 / x > 0 (3 )
From the definition field of divisor
x * ( 1 + x ) ≠ 0 (4 )
From inequality(1):
x > 0
From inequality(2):
x < 0 或 x > 0
From inequality(3):
x < -1 或 x > 0
From inequality(4):
x < -1 或 -1 < x < 0 或 x > 0
From inequalities (1) and (2)
x > 0 (5)
From inequalities (3) and (5)
x > 0 (6)
From inequalities (4) and (6)
x > 0 (7)
The final solution set is :
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