Take the derivative 


     -  =  + .


In the domain x >= 1  the derivative is always positive -- so, the function monotonically grows at x >= 1.


Therefore, the minimum of the function in this domain achieves at x = 1 and is equal to

     -  = 1 - 1 = 0.



The last step in solving such exercises is to make a plot


    

            Plot y =  - 


to make sure (visually) that our conclusions are correct.