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Assignment:Find the solution set of inequality (x+1)/(2x^2+5x-3) >= (x)/(4x^2-1) .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( x + 1 ) / ( 2 * x ^ 2 + 5 * x - 3 ) >= ( x ) / ( 4 * x ^ 2 - 1 ) (1)
From the definition field of divisor
2 * x ^ 2 + 5 * x - 3 ≠ 0 (2 )
From the definition field of divisor
4 * x ^ 2 - 1 ≠ 0 (3 )
From inequality(1):
-3 ≤ x ≤ -0.5 或 x ≥ 1/2
From inequality(2):
x < -3 或 -3 < x < 1/2 或 x > 1/2
From inequality(3):
x < -1/2 或 -1/2 < x < 1/2 或 x > 1/2
From inequalities (1) and (2)
-3 < x ≤ -0.5 或 x > 1/2 (4)
From inequalities (3) and (4)
-3 < x < -1/2 或 x > 1/2 (5)
The final solution set is :
-3 < x < -1/2 或 x > 1/2Your problem has not been solved here? Please take a look at the hot problems !