Question 778192: Solve: ((x+3)/(x)) > x
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! ((x+3)/(x)) > x
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[(x+3)/x]-x > 0
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[x+3-x^2]/x > 0
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(-x^2+x+3)/x > 0
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-(x^2-x-3)/x > 0
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Values of x that do not work: x = -1.3; x = 2.3; x = 0
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Draw a number line and plot -1.3,0,and 2.3
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Test a value in each of the resulting 4 number-line intervals.
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-(x^2-x-3)/x > 0
Test x = -10:: -/- > 0 ; true, so solutions in (-oo,-1.3)
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Test x = -1:: +/- > 0 ; false
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Test x = +1:: +/+ > 0 ; true, solutions in (0,2.3)
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Test x = +10:: -/+ > 0 ; false
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Solutions are listed above.
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Cheers,
Stan H.
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