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Assignment:Find the solution set of inequality 8*(x^3)/(((x^2)-1)^3)-(6*x)/(((x^2)-1)^2) >0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
8 * ( x ^ 3 ) / ( ( ( x ^ 2 ) - 1 ) ^ 3 ) - ( 6 * x ) / ( ( ( x ^ 2 ) - 1 ) ^ 2 ) >0 (1)
From the definition field of divisor
( ( x ^ 2 ) - 1 ) ^ 3 ≠ 0 (2 )
From the definition field of divisor
( ( x ^ 2 ) - 1 ) ^ 2 ≠ 0 (3 )
From inequality(1):
-7/7 < x < 0 或 x > 1/1
From inequality(2):
x < -1 或 -1 < x < 1 或 x > 1
From inequality(3):
x < -1 或 -1 < x < 1 或 x > 1
From inequalities (1) and (2)
-7/7 < x < -1 或 -1 < x < 0 或 1/1 < x < 1 或 x > 1 (4)
From inequalities (3) and (4)
-7/7 < x < -1 或 -1 < x < -1 或 -1 < x < 0 或 1/1 < x < 1 或 1 < x < 1 或 x > 1 (5)
The final solution set is :
-7/7 < x < -1 或 -1 < x < -1 或 -1 < x < 0 或 1/1 < x < 1 或 1 < x < 1 或 x > 1Your problem has not been solved here? Please take a look at the hot problems !