Lab rage impaired academic study (7)
I believe the answer is:
algebra
'academic study' is the definition.
'lab rage impaired' is the wordplay.
'impaired' indicates anagramming the letters.
'lab'+'rage'='labrage'
'labrage' with letters rearranged gives 'ALGEBRA'.
(Other definitions for algebra that I've seen before include "letters here set out the problem" , "Branch of maths - real bag (anag)" , "A garble (anag) - branch of mathematics" , "branch of learning" , "Symbolic maths" .)