SOLUTION: Solve the inequality [(x - 4)^3] / [x(x + 3)] is less than or equal to 0

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Question 378101: Solve the inequality [(x - 4)^3] / [x(x + 3)] is less than or equal to 0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Break up the number line into 4 regions using the critical points of the function.
Region 1:(-infinity,-3)
Region 2:(-3,0)
Region 3:(0,4)
Region 4:(4,infinity)
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For each region, choose a point in the region (not an endpoint).
Test the inequality.
If the inequality is satisfied, the region is part of the solution region.
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Region 1:x=-4
%28%28x+-+4%29%5E3%29+%2F+%28x%28x+%2B+3%29%29%3C=0+
%28-512%29%2F%28%28-4%29%28-1%29%29%3C0+
-128%3C0+
True, Region 1 is part of the solution region.
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Region 2:x=-2
%28%28x+-+4%29%5E3%29+%2F+%28x%28x+%2B+3%29%29%3C=0+
%28-216%29%2F%28%28-2%29%281%29%29%3C0+
108%3C0+
False, Region 2 is not part of the solution region.
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Region 3:x=1
%28%28x+-+4%29%5E3%29+%2F+%28x%28x+%2B+3%29%29%3C=0+
%28-27%29%2F%28%281%29%284%29%29%3C0+
-27%2F4%3C0+
True, Region 3 is part of the solution region.
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Region 4:x=5
%28%28x+-+4%29%5E3%29+%2F+%28x%28x+%2B+3%29%29+%3C=0+
%285%29%2F%28%285%29%288%29%29%3C0+
1%2F8%3C0+
False, Region 4 is not part of the solution region.
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Solution Region: (-infinity,-3)U(0,4)
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Graphical verification: Look for regions where the function is below the x-axis (y%3C0)
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