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Assignment:Find the solution set of inequality (x-1)/(x²-4x+5) >1 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( x - 1 ) / ( x ^ 2 - 4 * x + 5 ) >1 (1)
From the definition field of divisor
x ^ 2 - 4 * x + 5 ≠ 0 (2 )
From inequality(1):
2 < x < 3
From inequality(2):
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)
2 < x < 3 (3)
The final solution set is :
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