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[ 1/1Inequality]
Assignment:Find the solution set of inequality 1/(x+1)-1/(x-1) >2/x*x .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
1 / ( x + 1 ) - 1 / ( x - 1 ) >2 / x * x (1)
From the definition field of divisor
x + 1 ≠ 0 (2 )
From the definition field of divisor
x - 1 ≠ 0 (3 )
From the definition field of divisor
x ≠ 0 (4 )
From inequality(1):
-1 < x < 0 或 0 < x < 1
From inequality(2):
x < -1 或 x > -1
From inequality(3):
x < 1 或 x > 1
From inequality(4):
x < 0 或 x > 0
From inequalities (1) and (2)
-1 < x < 0 或 0 < x < 1 (5)
From inequalities (3) and (5)
-1 < x < 0 或 0 < x < 1 (6)
From inequalities (4) and (6)
-1 < x < 0 或 0 < x < 0 或 0 < x < 1 (7)
The final solution set is :
-1 < x < 0 或 0 < x < 0 或 0 < x < 1 Your problem has not been solved here? Please take a look at the hot problems !