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Assignment:Find the solution set of inequality (x^2+8/x^2+9)/(1+x^2) >0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( x ^ 2 + 8 / x ^ 2 + 9 ) / ( 1 + x ^ 2 ) >0 (1)
From the definition field of divisor
x ≠ 0 (2 )
From the definition field of divisor
1 + x ^ 2 ≠ 0 (3 )
From inequality(1):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(2):
x < 0 或 x > 0
From inequality(3):
x ∈ R (R为全体实数),即在实数范围内,不等式恒成立!
From inequalities (1) and (2)
x < 0 或 x > 0 (4)
From inequalities (3) and (4)
x < 0 或 x > 0 (5)
The final solution set is :
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