Egg whites will not whip if they come into contact with even the slightest trace of fat, grease or egg yolk. This is why it's a good idea when separating eggs to have three bowls: one for the yolks, one for the whites and one bowl to separate over so that you won't have to throw out a whole batch if one yolk breaks while separating. It is also a good idea to wash your hands, beaters and bowl before beginning as well, to make sure they are grease free.
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