\(S=\frac{5\left(x-1\right)}{4}+\frac{5}{x-1}+\frac{9\left(y-1\right)}{4}+\frac{9}{y-1}+\frac{7}{4}\left(x+y\right)+\frac{7}{2}\)
\(S\ge2\sqrt{\frac{25\left(x-1\right)}{4\left(x-1\right)}}+2\sqrt{\frac{81\left(y-1\right)}{4}}+\frac{7}{4}.6+\frac{7}{2}=28\)
\(\Rightarrow S_{min}=28\) khi \(x=y=3\)