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[ 1/1Inequality]
Assignment:Find the solution set of inequality 2^x/((2^x-4/3)(2^x-2/3)) >2^x/(2^x-1)^2 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality：
2 ^ x / ( ( 2 ^ x - 4 / 3 ) * ( 2 ^ x - 2 / 3 ) ) >2 ^ x / ( 2 ^ x - 1 ) ^ 2 (1)
From the definition field of divisor
( 2 ^ x - 4 / 3 ) * ( 2 ^ x - 2 / 3 ) ≠ 0 (2 )
From the definition field of divisor
2 ^ x - 1 ≠ 0 (3 )
From inequality(1)：
x < -0.584963 或 0.415037 < x < 8304967/500000 或 8304967/500000 < x < 673763/40000 或 673763/40000 < x < 20815937/1000000 或 20815937/1000000 < x < 22286121/1000000 或 x ＞ 22286121/1000000
From inequality(2)：
x < -0.584963 或 -0.584963 < x < 0.415037 或 x ＞ 0.415037
From inequality(3)：
x < 0 或 x ＞ 0
From inequalities (1) and (2)
x < -0.584963 或 或 0.415037 < x < 8304967/500000 或 8304967/500000 < x < 673763/40000 或 673763/40000 < x < 20815937/1000000 或 20815937/1000000 < x < 22286121/1000000 或 x ＞ 22286121/1000000 (4)
From inequalities (3) and (4)
x < -0.584963 或 0.415037 < x < 8304967/500000 或 8304967/500000 < x < 673763/40000 或 673763/40000 < x < 20815937/1000000 或 20815937/1000000 < x < 22286121/1000000 或 x ＞ 22286121/1000000 (5)
The final solution set is :
x < -0.584963 或 0.415037 < x < 8304967/500000 或 8304967/500000 < x < 673763/40000 或 673763/40000 < x < 20815937/1000000 或 20815937/1000000 < x < 22286121/1000000 或 x ＞ 22286121/1000000Your problem has not been solved here? Please take a look at the hot problems ！
