<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] I prefer to keep things in fractional form, and to try to get the same numerator to compare.
$$\frac{b}{c+d+b} = \frac{b}{c+d+b}\cdot\frac{\frac{1}{b}}{\frac{1}{b}}= \frac{\frac{b}{b}}{\frac{c+d+b}{b}}=\frac{1}{\frac{c}{b}+\frac{d}{b}+1}\lt\frac{1}{3}$$
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