First scoop a spoonful of water and pour it into the milk. At this time, the ratio of milk is 1/( 1+x), and the ratio of water is x/( 1+x).

Then scoop a spoonful from the milk and pour it into the water, and there will be milk in the water: x *1/(1+x) = x/(1+x).

The water in the milk cup is: x-x * x/(1+x) = x/(1+x).

So the two are equal.