Odgovor:
# X ^ 2 / ((x-1), (x + 2)) = 1 / (3 (x-1)) - 4 / (3 (x + 2)) *
Obrazloženje:
Moramo to napisati u smislu svakog čimbenika.
# X ^ 2 / ((x-1), (x + 2)) = A / (x-1), + B / (x + 2) *
# X ^ 2-A (x + 2) + B (x-1) #
Stavljanje # x = -2 #:
# (- 2) ^ 2-A (-2 + 2) + B (-2-1) #
# 4-3b #
# B = -4/3 #
Stavljanje # X = 1 #:
# 1 ^ 2-A (1 + 2) + B (1-1) #
# 1 = 3A #
# A = 1/3 #
# X ^ 2 / ((x-1), (x + 2)) = (1/3) / (x-1) + (- 4/3) / (x + 2) *
#COLOR (bijeli) (x ^ 2 / ((x-1), (x + 2))) = 1 / (3 (x-1)) - 4 / (3 (x + 2)) *
Odgovor:
# 1 + 1/3 * 1 / (1 x-) -4 / 3 * 1 / (x + 2) *
Obrazloženje:
# X ^ 2 / (x-1), (x + 2) #
=# (X-1), (x + 2) + x ^ 2- (x-1), (x + 2) / (x-1), (x + 2) #
=# 1 - (x-1), (x + 2) -X ^ 2 / (x-1), (x + 2) #
=# 1 (x-2) / (x-1), (x + 2) #
Sada sam rastavio frakciju u osnovne, # (X-2) / (x-1), (x + 2) = A / (x-1), + B / (x + 2) *
Nakon proširenja nazivnika, # A * (x + 2) + B * (x-1) = x-2 #
Set # x = -2 #, # 3b = -4 #, Dakle # B = 4/3 #
Set # X = 1 #, # 3A = -1 #, Dakle # A = -1/3 #
Stoga,
# (X-2) / (x-1), (x + 2) = - 1/3 * 1 / (x-1), + 4/3 * 1 / (x + 2) *
Tako, # X ^ 2 / (x-1), (x + 2) #
=# 1 (x-2) / (x-1), (x + 2) #
=# 1 + 1/3 * 1 / (1 x-) -4 / 3 * 1 / (x + 2) *
