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Assignment:Find the solution set of inequality (12.5*x*x/(4-x*x)-3*x*x+2)/(25*x/(4-x*x)-5*x) >(25*x*x*x*x/(4*(4-x*x)*(4-x*x))+(22*x*x+3*x*x/4+4)/(4-x*x)+2.5*x)/((-10*x*(1-5/(4-x*x)))/(4-x*x)) .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( 12.5 * x * x / ( 4 - x * x ) - 3 * x * x + 2 ) / ( 25 * x / ( 4 - x * x ) - 5 * x ) > ( 25 * x * x * x * x / ( 4 * ( 4 - x * x ) * ( 4 - x * x ) ) + ( 22 * x * x + 3 * x * x / 4 + 4 ) / ( 4 - x * x ) + 2.5 * x ) / ( ( -10 * x * ( 1 - 5 / ( 4 - x * x ) ) ) / ( 4 - x * x ) ) (1)
From the definition field of divisor
4 - x * x ≠ 0 (2 )
From the definition field of divisor
4 - x * x ≠ 0 (3 )
From the definition field of divisor
25 * x / ( 4 - x * x ) - 5 * x ≠ 0 (4 )
From the definition field of divisor
4 * ( 4 - x * x ) * ( 4 - x * x ) ≠ 0 (5 )
From the definition field of divisor
4 - x * x ≠ 0 (6 )
From the definition field of divisor
4 - x * x ≠ 0 (7 )
From the definition field of divisor
4 - x * x ≠ 0 (8 )
From the definition field of divisor
( -10 * x * ( 1 - 5 / ( 4 - x * x ) ) ) / ( 4 - x * x ) ≠ 0 (9 )
From inequality(1):
-2 < x < -0.424429 或 2 < x < 9.424429
From inequality(2):
x < -2 或 -2 < x < 2 或 x > 2
From inequality(3):
x < -2 或 -2 < x < 2 或 x > 2
From inequality(4):
x < -2 或 -2 < x < 0 或 0 < x < 2 或 x > 2
From inequality(5):
x < -2 或 -2 < x < 2 或 x > 2
From inequality(6):
x < -2 或 -2 < x < 2 或 x > 2
From inequality(7):
x < -2 或 -2 < x < 2 或 x > 2
From inequality(8):
x < -2 或 -2 < x < 2 或 x > 2
From inequality(9):
x < 0 或 x > 0
From inequalities (1) and (2)
-2 < x < -2 或 -2 < x < -0.424429 或 x < -2 或 2 < x < 9.424429 (10)
From inequalities (3) and (10)
-2 < x < -2 或 -2 < x < -0.424429 或 2 < x < 9.424429 (11)
From inequalities (4) and (11)
-2 < x < -2 或 -2 < x < -0.424429 或 2 < x < 9.424429 (12)
From inequalities (5) and (12)
-2 < x < -2 或 -2 < x < -0.424429 或 2 < x < 2 或 2 < x < 9.424429 (13)
From inequalities (6) and (13)
-2 < x < -2 或 -2 < x < -0.424429 或 2 < x < 2 或 2 < x < 9.424429 (14)
From inequalities (7) and (14)
-2 < x < -2 或 -2 < x < -0.424429 或 2 < x < 2 或 2 < x < 9.424429 (15)
From inequalities (8) and (15)
-2 < x < -2 或 -2 < x < -0.424429 或 2 < x < 2 或 2 < x < 9.424429 (16)
From inequalities (9) and (16)
-2 < x < -2 或 -2 < x < -0.424429 或 2 < x < 2 或 2 < x < 9.424429 (17)
The final solution set is :
-2 < x < -2 或 -2 < x < -0.424429 或 2 < x < 2 或 2 < x < 9.424429 Your problem has not been solved here? Please take a look at the hot problems !