difference between take care of and look after

take care of - анхаарал тавих

take care (informal)

used when saying goodbye

• Bye! Take care!

take care (that..../ to do something)

to be careful

• Take care (that) you don't drink too much!

take care of someone/something/yourself

to care for someone or something/yourself; to be careful about something

• Who's taking care of the children while you are away?
• she takes care of her clothes
• he's old enough to take care of himself

look after - асрах, харах

look after yourself / someone / something

1 to be responsible (итгэх, найдах) for or to take care of someone or something

• Who is going to look after the children while you are away?
• Don't worry about me - i can look after myself

2 to make sure that things happen to someone advantage

• He is good at looking after his own interests

What's the difference between "Take Care Of" and "Look After"?

1. If I say "take care of a person" or "look after a person", it usually means the same thing, to provided care over a period for a person. 
   It is not always true, however. 
   "Take care of a person" can also be used to mean providing a resolution(шийдвэрлэлт) to a person's request or problem. It implies(илэрхийлэх) a short term solution. 
   "This customer has a request concerning(сонирхох) the new computer. Could you please take care of them." 
   In this case the person being spoken to is being asked to give advice or short-term help to the costumer, not provide care. 
   Sometimes you will hear "look after" in this regard, but not as often. 
   You would also "take care" (resolve(шийдвэрлэх)) a problem. 
   Again, there is considerable(үлэмжхэн) overlap(давхцал) here, so you would not be guilty of some huge error if you interchanged the two,.