Question 85112
Solve the rational inequality and graph the solution set on a real number line.

x-6
---- > 0
x+1

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The fraction is >0 when both numerator and denominator are positive 
or when both numerator and denominator are negative.
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So you determine when the numerator and the denominator are zero:
That occurs when x=6 or when x=-1
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You draw a number line and plot the two values x=-1 and x=6.
You do this because you know those values are not part of the solution.
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Those numbers break the number line into three intervals:
(-inf,-1) , (-1,6), (6,+inf)
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Look for solution values in those three intervals by selecting a test value
for each and substituting into (x-6)/(x+1):
Interval (-inf,-1); pick x=-100; you get (-)/(-) which is >0
this whole interval is part of the solution.
-------
Interval (-1,6); pick x=0; you get (-)/(+) which is <0
this whole interval contains no solutions.
-------------
Interval (6,+inf); pick x=100; you get (+)/(+) which is >0
this whole interval is part of the solution
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Final graph
Darken the intervals where the solutions lie:
(-inf,-1) OR (6,+inf)
Draw a circle around the points x=-1 and x=6 as they are NOT
part of the solution.
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Cheers,
Stan H.