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College Algebra/Inequalities

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solve the inequality
x+3/x-2 less then or equal to 0

  • College Algebra/Inequalities -

    suspect you mean
    (x+3) / (x-2) </= 0
    first let's look at the singularity when x = 2
    when x is a little above 2 we have 5/+0
    which is +oo
    when x is a little below 2 we have 5/-0 which is -oo
    so to the right of x = 2 it is +, no matter how big x gets
    to the left of x = 2, it is -
    until x = -3
    then it is zero
    to the left of x = -3, it is + again
    SO
    it is only - between x = -3 and x = 2
    -3 </= x </= +2

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