$y =f(x) =(ax^2 + bx +c)/(dx^2+ex+f)$ We have to find the conditions for this it takes all real values.

Question

$$ y=f(x)=\frac{ax^2+bx+c}{dx^2+ex+f} $$ We have to find the conditions for this it takes all real values.

MY solution

One approach is to equate it to y and for a quadratic of x and put discriminant greater than equal to 0..That is very lengthy.Is their any better method..?

Answer 1

Find the numbers that make the bottom zero. You can't divide by zero.