(x ^ 2-5x-6) / (x ^ 3 + ax ^ 2 + bx + c) se simplifica a 1 / (x-2), luego a + b + c =?

Responder:

#a + b + c = 9 #

Dado: # (x ^ 2-5x-6) / (x ^ 3 + ax ^ 2 + bx + c) = 1 / (x-2) #

Resulta que:

# (x ^ 2-5x-6) (x-2) = x ^ 3 + ax ^ 2 + bx + c #

Multiplicar

#x (x ^ 2-5x-6) - 2 (x ^ 2-5x-6) = x ^ 3 + ax ^ 2 + bx + c #

# x ^ 3-5x ^ 2-6x - 2x ^ 2 + 10x + 12 = x ^ 3 + ax ^ 2 + bx + c #

Combina términos semejantes:

# x ^ 3-7x ^ 2 + 4x + 12 = x ^ 3 + ax ^ 2 + bx + c #

Coeficientes de coincidencia:

#a = -7, b = 4, yc = 12 #

#a + b + c = -7+ 4 + 12 #

#a + b + c = 9 #