Math

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How to solve this:

((x-3)(x+2))/((x-1)) < 0

I don't understand since theres x-1 in the denominator

  • Math -

    The critical values are -2, 1 ,and 3 , with of course x ? 1
    I then pick an arbitrary value in each of the regions and determine the sign of the answer, the actual answer does not matter.
    e.g let x = -5
    (-)(-)/(-1) < 0 , so x <-2 works
    let x = 0 , a value between -2 and 1
    (-3)(+).(-) > 0 , no good
    let x = 2 , a value between 1 and 3
    (-)(+)/(+) < 0 , good
    let x = 5 , a value > 3
    (+)(+)/(+) > 0 , no good
    so
    x < -2 OR 1 < x < 3

  • Math -

    so for this: (-)(-)/(-1) < 0 , so x <-2 works

    you replace the 0 with -2 ? .

    Also for this part let x = 5 , a value > 3
    (+)(+)/(+) > 0 , no good

    you had to change the sign because it was all positive?

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