<s>[INST] Which expressions is greater, $\frac{b}{c+d+b}$ or $\frac{1}{3}$? There are 3 kinds of animals: Cats, dogs, bears. # of cats is $c$, # of dogs is $d$ and # of bears is $b$. It's said that $$c>d>b.$$ The question is: 

Which expression is greater $\dfrac{b}{c+d+b}$ or $\dfrac{1}{3}$?

The thing that I didn't understand is what $\dfrac{b}{c+d+b}$ actually means. And how can I solve for it?
 [/INST] Since $$c\gt d\gt b$$ we have
$$c+d+b\gt b+b+b=3b$$
As $c,d,b\ge 0$,
$$\frac{1}{c+d+b}\lt\frac{1}{3b}$$
$$\frac{b}{c+d+b}\lt\frac{b}{3b}$$
$$\frac{b}{c+d+b}\lt\frac{1}{3}$$
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