Question Number 143122 by loveineq last updated on 10/Jun/21
![Let a,b ∈[0,1] and a+b ≤ 1. Prove that (1/(1+a))+(1/(1+b))+(1/2) ≤ (2/(a+b))](https://www.tinkutara.com/question/Q143122.png)
$$\mathrm{Let}\:{a},{b}\:\in\left[\mathrm{0},\mathrm{1}\right]\:\mathrm{and}\:{a}+{b}\:\leqslant\:\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}+{a}}+\frac{\mathrm{1}}{\mathrm{1}+{b}}+\frac{\mathrm{1}}{\mathrm{2}}\:\leqslant\:\frac{\mathrm{2}}{{a}+{b}}\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$