SOLUTION: Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. x-9/x+1 >0

Question 156259: Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation.
x-9/x+1 >0
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation.
x-9/x+1 >0
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x cannot be 0 and x cannot be -1
Draw a number line and plot x = -1 and x = 0 on it.
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Check a test value from each resulting number-line interval in the inequality.
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Let x = -2; you get (-2-9)/(-2+1) >0; true, so solutions in (-inf,-1)
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Let x = (-1/2); you get (-1/2 -9)/(-1/2 +1) > 0; false, no solutions in (-1,0)
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Let x = 1; you get (1-9)/(1+1) >0 ; false, no solutions in (0,+inf)
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Final solution: {x| x < -1}
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Cheers,
Stan H.
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