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Math Help - Abstract Inequalities

  1. #1
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    Abstract Inequalities

    Can anyone help me confirm if I've solved this correctly?

    Many thanks.

    Q.
    If a, b, c, d are positive numbers & \frac{a}{b}>\frac{c}{d}, prove that \frac{a+c}{b+d}>\frac{c}{d}.

    Attempt: 1st: if \frac{a}{b}>\frac{c}{d}
    if ad>bc...true

    2nd: if \frac{a+c}{b+d}>\frac{c}{d}
    if ad+cd>bc+cd
    if ad>bc...true
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  2. #2
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    Re: Abstract Inequalities

    Quote Originally Posted by GrigOrig99 View Post
    Can anyone help me confirm if I've solved this correc

    Q.
    If a, b, c, d are positive numbers & \frac{a}{b}>\frac{c}{d}, prove that \frac{a+c}{b+d}>\frac{c}{d}.
    From the given
    \begin{align*}ad &>bc\\ ad+cd &> bc+cd\\(a+c)d &>(b+d)c\\ \frac{a+c}{b+d}&>\frac{c}{d}  \end{align*}.
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  3. #3
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    Re: Abstract Inequalities

    Great. Thank you.
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