$\displaystyle \lim_{x\to 1}\left(\frac{x}{x - 1} - \frac{1}{\ln x}\right)$.

I worked out that it was an interminate difference of the form ∞ - ∞, so I figured I have to differentiate xlnx - x + 1 / (x-1)(lnx), but then the answer will be reaaally long, and I dont know what to do. This sometimes happens when I try to differentiate something