Wat is ((3x ^ 2 - 7x - 6) / (x ^ 3 - 3x ^ 2 + 4s-12)) / ((3x ^ 2 - 4x - 4) / (x ^ 4 - 16))?

Wat is ((3x ^ 2 - 7x - 6) / (x ^ 3 - 3x ^ 2 + 4s-12)) / ((3x ^ 2 - 4x - 4) / (x ^ 4 - 16))?
Anonim

Antwoord:

(x + 2)

Uitleg:

#f (x) = (a / b) / (c / d) #

Factor alle functies van x:

1. #a = 3x ^ 2 - 7x -6 = # (3x + 2) (x - 3)

2. #b = x ^ 3 - 3x ^ 2 + 4x - 12 = (x - 3) (x ^ 2 + 4) #

3. #c = 3x ^ 2 - 4x - 4 = # (3x + 2) (x - 2)

4. #d = x ^ 4 - 16 = (x ^ 2 + 4) (x - 2) (x + 2) #

#f (x) = (3x + 2) (x - 3) / (x - 3) (x ^ 2 + 4) (x ^ 2 + 4) (x - 2) (x + 2) / (3x + 2) (x - 2) #

f (x) = (x + 2)