The most common cause of plants developing brown leaf edges is over or under watering.  A good way to tell if your house plant needs water is to lift the pot and feel how heavy it is. If it is light it needs water. With a little practice one can learn how heavy the pot is when it is damp but not wet, or dry and needs water. 
Because the edges of your plant have died it probably did not get enough water and was very dry at one point. 
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