# Thread: Help with proving an inequality

1. ## Help with proving an inequality

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

2. Originally Posted by flower3
$\displaystyle if \ \frac {a}{b} < \frac{c}{d} \ show \ that \ : \ \frac{a}{b}<\frac{a+c}{b+d}<\frac{c}{d} .... b,d>0$
Here is one-half of it.
$\displaystyle \begin{gathered} \frac{a} {b} < \frac{c} {d} \hfill \\ ad < bc \hfill \\ ab + ad < ab + bc \hfill \\ a(b + d) < b(a + c) \hfill \\ \frac{a} {b} < \frac{{a + c}} {{b + d}} \hfill \\ \end{gathered}$