When we have the following inequality:
$$\frac{a}{b+c} \ge \frac{d}{e+c},$$
with $a,b,c,d,e \in \mathbb R_{\ge 0}$
Then it seems to hold that
$$\frac{a}{b} \ge \frac{d}{e},$$
Is this correct? Does it also work in the other direction (iff)?
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The answer by @Did answers the question,but I forgot to add some other conditions. I will ask a new question. – miselico Mar 24 '14 at 17:41
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New question at http://math.stackexchange.com/questions/725040/subtracting-positive-numbers-from-denominator-in-an-inequality-with-conditions – miselico Mar 24 '14 at 18:09
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$$\frac{\color{blue}{3}}{\color{blue}{2}}\lt\frac{\color{green}{2}}{\color{green}{1}}\quad\&\quad\forall\color{red}{c}\gt1,\quad\frac{\color{blue}{3}}{\color{blue}{2}+\color{red}{c}}\gt\frac{\color{green}{2}}{\color{green}{1}+\color{red}{c}}$$
Did
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Could you switch back to the previous answer you wrote? It is just slightly more straightforward and answers the question. – miselico Mar 24 '14 at 17:42
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