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Math Help - Help with proving an inequality

  1. #1
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    Help with proving an inequality

     if \ \frac {a}{b} < \frac{c}{d}  \ show \ that \ : \ \frac{a}{b}<\frac{a+c}{b+d}<\frac{c}{d} .... b,d>0
    Last edited by mr fantastic; October 9th 2009 at 10:18 PM. Reason: Changed post title
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  2. #2
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    Quote Originally Posted by flower3 View Post
     if \ \frac {a}{b} < \frac{c}{d}  \ show \ that \ : \ \frac{a}{b}<\frac{a+c}{b+d}<\frac{c}{d} .... b,d>0
    Here is one-half of it.
    \begin{gathered}<br />
  \frac{a}<br />
{b} < \frac{c}<br />
{d} \hfill \\<br />
  ad < bc \hfill \\<br />
  ab + ad < ab + bc \hfill \\<br />
  a(b + d) < b(a + c) \hfill \\<br />
  \frac{a}<br />
{b} < \frac{{a + c}}<br />
{{b + d}} \hfill \\ <br />
\end{gathered}
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