<s>[INST] Can we say that $\frac{a+b}{c+d} \leq \frac{a}{c} + \frac{b}{d} $ If $a,b,c,d$ are positive real numbers, can we say that $\frac{a+b}{c+d} \leq \frac{a}{c} + \frac{b}{d} $ is always true? If no, can you please give insignts on under which conditions this might be true. 
Any references to a similar type of inequalities are also welcome
Thank you, 
 [/INST] Solution to new version:
Since $$\frac{a}{c+d}  \leq \frac{a}{c}$$
and
$$\frac{b}{c+d}  \leq \frac{b}{d}$$
we have
$$\frac{a+b}{c+d} = \frac{a}{c+d} + \frac{b}{c+d} \leq \frac{a}{c} + \frac{b}{d} $$
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