Determine the vertical asymptotes and horizontal asymptotes

Determine the vertical asymptotes and horizontal asymptotes (if there are any) of the following functions. a) f(x) = x-4/(x^2 - x - 2)(x + 4) b) f(x) = 6x^2 + 3x + 1/3x^2 - 5x - 2

Solution

F(x) = (x-4) / ( x² - x -2) ( x+4)

F(x) = (x-4)/ ( x² -2x + x -2) (x+4)

F(x) = (x-4) / (x+1) (x-2) (x+4)

For vertical asymptotes

Put denominator = 0

X+1 = 0 , x-2 = 0 , x+4 = 0

VA: X= -1 , x= 2 , x= -4

For Horizontal asymptotes

Since degree of denominator is greater than degree of numerator

So horizontal asymptotes

HA : Y= 0