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