\(\frac{2}{b}=\frac{1}{a}+\frac{1}{c}\ge\frac{4}{a+c}\)
\(\frac{a}{b}+\frac{c}{b}\le2\Leftrightarrow x+y\le2\)
VT=\(\frac{x+1}{2x-1}+\frac{y+1}{2y-1}\)
\(2VT=2+3\left(\frac{1}{2x-1}+\frac{1}{2y-1}\right)\ge2+\frac{3.4}{2\left(x+y\right)-2}\ge8\)
=> dpcm