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Math Help - Solving a Rational Inequality

  1. #1
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    Solving a Rational Inequality

    Using Analytical method, find the solution set of the inequality \frac{3}{x-1}+\frac{5}{(x-2)^2} > \frac{3}{x-2}
    Last edited by Punch; May 7th 2011 at 10:46 PM.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Punch View Post
    Using Analytical method, find the solution set of the inequality \frac{3}{x-1}+\frac{5}{x-2}^2 > \frac{3}{x-2}
    Getting a common denominator gives and moving everything to the right hand side gives

    0 > \frac{3(x-1)-3(x+2)-5(x-1)}{(x-1)(x-2)}=\frac{-5x-4}{(x-1)(x-2)}

    So the inequality will change signs at

    x=1 \quad x=2 \quad x=-\frac{4}{5}

    can you finish from here?
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  3. #3
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    Thank you so much, but could u help me with one other thing? What does analytical method mean? i tried googling but only found definitions that i could not understand
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by Punch View Post
    Thank you so much, but could u help me with one other thing? What does analytical method mean? i tried googling but only found definitions that i could not understand
    Loosely speaking it means to find an exact solution using algebra calculus ect.

    What it is saying is don't plot a graph and estimate ect.
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