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Math Help - Inequalities: Variable in Denominator both sides

  1. #1
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    Inequalities: Variable in Denominator both sides

    Please tell me how this question will be solved

    1/(x+2) > 3/(x-3)

    answer: (-9/2, -2) U (3,+infinity)

    Though i know the answer but i dont how how will get it

    Thanx
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  2. #2
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    Re: Inequalities: Variable in Denominator both sides

    Quote Originally Posted by bajpaiapurva View Post
    Please tell me how this question will be solved

    1/(x+2) > 3/(x-3)

    answer: (-9/2, -2) U (3,+infinity)

    Though i know the answer but i dont how how will get it

    Thanx
    \frac1{x+2}>\frac3{x-3}~\implies~\frac{x-3-3(x+2)}{(x+2)(x-3)}>0

    Examine when a fraction is greater than zero.

    If + means positive (> 0) and - means negative (<0) you'll get the following cases:

    \frac{+}{+ \cdot +}~\vee~\frac{+}{- \cdot -} ~\vee~\frac{-}{+ \cdot -}~\vee~\frac{-}{- \cdot +}

    Each fraction describes 3 inequalities.
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    Re: Inequalities: Variable in Denominator both sides

    Quote Originally Posted by bajpaiapurva View Post
    Please tell me how this question will be solved
    \frac{1}{(x+2)} > \frac{3}{(x-3)}

    answer: (-9/2, -2) \cup (3,\infty)
    Though i know the answer but i dont how how will get it
    Thanx
    That answer is incorrect. It includes x=5 which does not work.

    The given answer works for \frac{1}{(x+2)} < \frac{3}{(x-3)}.

    Please check the post.
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