Help with proving an inequality

**flower3** · Oct 9th 2009, 12:22 PM

$if \ \frac {a}{b} < \frac{c}{d} \ show \ that \ : \ \frac{a}{b}<\frac{a+c}{b+d}<\frac{c}{d} .... b,d>0$

**Plato** · Oct 9th 2009, 12:34 PM

Originally Posted by flower3

$if \ \frac {a}{b} < \frac{c}{d} \ show \ that \ : \ \frac{a}{b}<\frac{a+c}{b+d}<\frac{c}{d} .... b,d>0$

Here is one-half of it.
$\begin{gathered} \frac{a} {b} < \frac{c} {d} \hfill \\ ad < bc \hfill \\ ab + ad < ab + bc \hfill \\ a(b + d) < b(a + c) \hfill \\ \frac{a} {b} < \frac{{a + c}} {{b + d}} \hfill \\ \end{gathered}$

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