How to show that $\frac{x^2}{x-1}$ simplifies to $x + \frac{1}{x-1} +1$ How does $\frac{x^2}{(x-1)}$ simplify to $x + \frac{1}{x-1} +1$?
The second expression would be much easier to work with, but I cant figure out how to get there.
Thanks

$$\frac{x^2}{x-1}=\frac{x^2-x+x-1+1}{x-1} = \frac{x(x-1) + (x-1)+1}{x-1}=\frac{x(x-1)}{x-1}+\frac{x-1}{x-1}+\frac{1}{x-1}$$
