设函数\(f\left( x \right)={\ln }x+\dfrac{a}{x-1}\) \(\left( a > 0,\ln 2\approx 0.69 \right)\)
\((\)Ⅰ\()\)当\(a=\dfrac{1}{30}\)时,求函数\(f\left( x \right)\)的单调区间;
\((\)Ⅱ\()\)当\(a\geqslant \dfrac{1}{2}\),\(x\in \left( 1,+\infty \right)\)时,求证:\({\ln }x+\dfrac{a}{x-1} > 1\).