2014/040) Let x,y,z be not necessarily distinct integers between 1 and 2011, inclusive. Find the smallest possible value of (xy+z)/(x+y+z).

xy+zx+y+z
= 1+xy−x−yx+y+z
= 1+(x−1)(y−1)−1x+y+z

(x-1)(y-1) - 1 is positive for all x and y except for x=1 or y=1 ( in the condition x, y <= 2011)

so x =1 , and y = 1

so we get given expression
= 1−12+z
z = 1 shall make it lowest

so x = 1 = y = z shall give the value 23