Válasz:
# 3x + (x-1) / (x ^ 2 + 1) #.
Magyarázat:
Figyelje meg, hogy # 3x ^ 3 + 4x-1 #.
# = 3x ^ 3 + 3x + x-1 #, # = 3x (x ^ 2 + 1) + (X-1) #.
#:. (3x ^ 3 + 4x-1) / (x ^ 2 + 1) = {3x (x ^ 2 + 1) + (X-1)} / (x ^ 2 + 1) #, # = {3x (x ^ 2 + 1)} / (x ^ 2 + 1) + (X-1) / (x ^ 2 + 1) #, # rArr (3x ^ 3 + 4x-1) / (x ^ 2 + 1) = 3x + (x-1) / (x ^ 2 + 1) #.
