Let $\displaystyle a>1$ and let $\displaystyle f: (1,2] \rightarrow \mathbb{R}$ be defined by $\displaystyle f(x)=\frac{x}{x-1}$. Prove that $\displaystyle f$ is uniformly continuous on the interval $\displaystyle [a,2]$, but $\displaystyle f$ is not uniformly continuous on $\displaystyle (1,2]$.

I am lost on this problem. Any help is appreciated. Thanks in advance.