You can put this solution on YOUR website! (x-5)/(x^2-16)>0
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Let's solve for the inequality first.
We factor the denominator and get (x-4)(x+4)
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Now we draw a number line and draw a line through it at -4, 4, and 5.
We have to find out whether our equation is positive or negative on either side of those lines.
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let x=-5: -10/(25-16) is negative so when x<-4 the equation is <0. when x=-4 we would have division by zero.
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let x=0: -5/-16 is positive so when -4>x<4: (x-5)/(x^2-16)>0
when x=4 we get another division by zero.
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let x = 4.5: -.5/4.25 is negative so the equation is <0 between 4 and 5.
When x=5 the equation = 0.
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let x=6: 1/20 is positive so when x>5: (x-5)/(x^2-16)>0
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X(-4,4)U(5,infinity)
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I tried to do the graph on our graphing utility but it didn't come out.
Ed
