I need to calculate the equation in form of $$ f(x)= \frac{ax^2+bx+c}{px^2+bx+c} $$ The asymptote has these properties:
- Vertical asymptotes on x = 2 and x = 1
- Horizontal asymptote on y = 0
- It went through (-2,0) and (0,-1)
I've tried doing the vertical using $$ px^2+qx+r = p (x-2) (x-1) = p (x^2-3x+2) $$ and the horizontal using $$ \frac{a}{p}=0 $$ meaning that the value of a = 0 I've also tried to calculate where it intersects x with $$ ax^2+bx+c=a(x+2) $$ What I'm confused with are the steps after that.