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[ 1/1Inequality]
Assignment:Find the solution set of inequality 1/(x+absx)+1/(x-absx) <100000 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
1 / ( x + abs x ) + 1 / ( x - abs x ) <100000 (1)
From the definition field of divisor
x + abs x ≠ 0 (2 )
From the definition field of divisor
x - abs x ≠ 0 (3 )
From inequality(1):
The solution set is empty, that is, within the range of real numbers, the inequality will never be established!
From inequality(2):
x < -433889/500000 或 -433889/500000 < x < -787901/1000000 或 -787901/1000000 < x < -28321/40000 或 -28321/40000 < x < -157037/250000 或 -157037/250000 < x < -34267/62500 或 -34267/62500 < x < -93679/200000 或 -93679/200000 < x < -388519/1000000 或 -388519/1000000 < x < -154321/500000 或 -154321/500000 < x < -45753/200000 或 -45753/200000 < x < -148889/1000000 或 x > -148889/1000000
From inequality(3):
x < 679/62500 或 679/62500 < x < 90741/1000000 或 90741/1000000 < x < 1706/9999 或 1706/9999 < x < 125247/500000 或 125247/500000 < x < 33037/100000 或 33037/100000 < x < 410247/1000000 或 410247/1000000 < x < 490123/1000000 或 490123/1000000 < x < 57/100 或 57/100 < x < 649877/1000000 或 x > 649877/1000000
The final solution set is :
The solution set is empty,that is, the inequality will never be estatlished within the real number range.
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