Question 62776
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solve the rational inequality (x-2)/(x+3) <= 0
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They want you solve this inequality

    {{{(x-2)/(x+3)}}} <= 0.    (1)


The left side rational function can be non-positive if and only if

    EITHER the numerator is non-positive and denominator is positive

        x - 2 <= 0  and  x + 3 > 0    (2)

    OR     the numerator is non-negative and denominator is negative

        x - 2 >= 0  and  x + 3 < 0.   (3)



In case (2),  x <= 2  and  x > -3  simultaneously, or  

              -3 < x <= 2.



In case (3),  x >= 2  and  x < -3 simultaneously,  which has no solutions.  



Thus the final solution to the given inequality is this set of real numbers  -3 < x <= 2,
or, in the interval notation, the set (-3,2].
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Solved.