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[ 1/1Inequality]
Assignment:Find the solution set of inequality (1/2/(1-a))*(1/2/(1-a))+1/(4*a)*(2-a)/(1-a) <0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( 1 / 2 / ( 1 - a ) ) * ( 1 / 2 / ( 1 - a ) ) + 1 / ( 4 * a ) * ( 2 - a ) / ( 1 - a ) <0 (1)
From the definition field of divisor
1 - x ≠ 0 (2 )
From the definition field of divisor
1 - x ≠ 0 (3 )
From the definition field of divisor
4 * x ≠ 0 (4 )
From the definition field of divisor
1 - x ≠ 0 (5 )
From inequality(1):
a < 0
From inequality(2):
a < 1 或 a > 1
From inequality(3):
a < 1 或 a > 1
From inequality(4):
a < 0 或 a > 0
From inequality(5):
a < 1 或 a > 1
From inequalities (1) and (2)
a < 0 (6)
From inequalities (3) and (6)
a < 0 (7)
From inequalities (4) and (7)
a < 0 (8)
From inequalities (5) and (8)
a < 0 (9)
The final solution set is :
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