Do well to study question, eliminating unknown component (7)
I believe the answer is:
conquer
'eliminating unknown component' is the definition.
I can't tell whether this defines the answer.
'do well to study question' is the wordplay.
'do well' becomes 'er' (I am not sure about this - if you are sure you should believe this answer much more).
'to' says to put letters next to each other (I've seen this in other clues).
'study' becomes 'con' (con can mean to study).
'question' becomes 'qu' (abbreviation).
'con'+'qu'='conqu'
'er' after 'conqu' is 'CONQUER'.
Can you help me to learn more?
(Other definitions for conquer that I've seen before include "Overcome militarily" , "Beat" , "Crush" , "Overcome by force" , "worst" .)