SOLUTION: solve x+7/x-2 < 0.

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Question 234607: solve x+7/x-2 < 0.
Found 2 solutions by RAY100, solver91311:
Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
x +7/(x-2) <0
.
multiply by (x-2)
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x(x-2) +7 <0
.
x^2 -2x +7 <0
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solve by quadratic formula
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a=1,,,b--2,,,,c=7
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x=[ -(-2)+/- sqrt{(-2)^2 -4(1) (7)}]/2(1)
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x=[ 2 +/- sqrt{4-28}]/2
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x= 1 +/- 2.45i,,,,,
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returning to x^2 -2x +7<0
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(x-1 -2.45i)(x-1+2.45i) <0
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x-1-2.45i <0,,,,,x< 1+2.45i
.
x-1+2.45i <0,,,,,x< 1-2.45i
.







Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The fraction will be positive, or greater than zero whenever the signs in the numerator and denominator are the same, and the fraction will be less than zero whenever the signs are different.

So whenever , and whenever . Since , both the numerator and denominator are positive -- and therefore the entire fraction is positive -- whenever .

whenever and whenever . Since , both numerator and denominator are negative, and therefore the entire fraction is positive, whenever .

Now we can see that whenever , the numerator of will be positive and the denominator will be negative making the value of the entire fraction negative. Note that is NOT in the solution set, because this value makes the value of the fraction exactly zero.


John