parmenides51 wrote: Let $a$ and $b$ be real numbers with $0 \le a, b \le 1$. (a) Prove that $ \frac{a}{b+1} +\frac{b}{a+1} \le 1.$ (b) Find the case of equality. $$ \frac{a}{b+1} +\frac{b}{a+1} \leq\frac{a}{b+a}+\frac{b}{a+b}=1$$Equality holds when $ a=b=1.$