<s>[INST] Let $a,b,c >0$ Prove the inequality $\displaystyle{\frac{a}{a+1}+\frac{b}{b+1}+\frac{c}{c+1}+\frac{1}{a+b+c+1} \geq 1}$ Let $a,b,c >0$ 
Prove the inequality $\displaystyle{\frac{a}{a+1}+\frac{b}{b+1}+\frac{c}{c+1}+\frac{1}{a+b+c+1} \geq 1}$
I dont even know where to begin.
Only interested in hints (not solution)
 [/INST] Hint :
$$\frac{a}{a+1} > \frac{a}{a+b+c+1}$$
$$\frac{b}{b+1} > \frac{b}{a+b+c+1}$$
$$\frac{c}{c+1} > \frac{c}{a+b+c+1}$$
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