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Math Help - Rational Function Inequality

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    Rational Function Inequality

    3x-5

    ______ -1 is less than or equal to 0


    x - 3


    Doesn't the -1 change everything? What would be a zero normally, is now a negative one. So should I find the zeros without considering the -1 then add 1 to the zeros and call it good? No, because the multiplication wouldn't work correctly... Please help, and thanks.
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    Quote Originally Posted by Isimbot View Post
    3x-5

    ______ -1 is less than or equal to 0


    x - 3


    Doesn't the -1 change everything? What would be a zero normally, is now a negative one. So should I find the zeros without considering the -1 then add 1 to the zeros and call it good? No, because the multiplication wouldn't work correctly... Please help, and thanks.
    \frac{3x-5}{x-3} - 1 \le 0

    \frac{3x-5}{x-3} - \frac{x-3}{x-3} \le 0

    \frac{2x-2}{x-3} \le 0

    critical values ...

    x = 1 and x = 3

    for x <  1 ... the inequality is false

    for 1 < x < 3 ... the inequality is true

    for x > 3 ... the inequality is false

    solution set is 1 \le x < 3
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