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

Hint: An alternative method would be to compute: $$\frac{x^2}{x-1}-\left(x+1+\frac1{x-1}\right)$$
And then conclude that since $$\frac{x^2}{x-1}-\left(x+1+\frac1{x-1}\right)=0$$
Then $$\frac{x^2}{x-1}=x+1+\frac1{x-1}.$$
