A= $\frac{a+1+1}{a+1}+\frac{-(2b+1)+2}{1+2b}$ =1+$\frac{1}{a+1} -1+\frac{2}{1+2b} =\frac{1}{a+1} +\frac{1}{\frac{1}{2}+b}$ $\geq \frac{4}{a+b+\frac{1}{2}+1} \geq \frac{4}{2+\frac{1}{2}+1} =\frac{8}{7}$
dấu "="$\Leftrightarrow a=\frac{3}{4} b=\frac{5}{4}$