Question 719218
(-(x-1)^2(2-x))/((3-x)(5x-1)^2) >= 0
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1st: Solve the EQUALITY:
-(x-1)^2(2-x) = 0
x = 1 or x = 2
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2nd: Note value that x cannot take:
x = 3 or x = 1/5
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3rd: Solve the INEQUALITY:
Draw a number line and plot x = 1/5, x = 1, x = 2, x = 3
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Test a value in each of the resulting 5 number line intervals
to find solution intervals:
(-(x-1)^2(2-x))/((3-x)(5x-1)^2) > 0
If x=0 you get: [-(-1)^2(2)]/[(3*(-1)^2] = -2/3 is not > 0
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If x=1/2 you get: [-(-1/2)^2(3/2)]/[(5/2)(3/2)^2] = (-3/8)/+ is not > 0
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If x = 3/2 the result is not > 0
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If x = 5/2 the result IS > 0
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If x = 10 the result is not > 0
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Conclusion:
Solution: x = 1 or values in the interval [2,3)
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{{{graph(400,400,-10,10,-10,10,(-(x-1)^2(2-x))/((3-x)(5x-1)^2) >= 0)}}}
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Cheers,
Stan H.
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