Hello, I wonder if anyone can help me, would be very grateful if anyone could.

If you wanted to find the range of a curve say y=(2x^2

+ 5x+3)/(4x^2 + 5x +3) instead of using calculus to find the stationary points and then subing back in to find e.g. the min. value of y or whatever, you can rearrange :

(4y-2)x^2 + (5y-5)x + 3y-3 =0 and then using b^2 - 4ac>0 to find the possible range...

just wondered...when does this method fail? It failed when I tried to use it for some other questions like y=[(x-1)(3x+2)]/[(x+1)^2] and pretty certain I didn't make any algebraic slip ups there.

Anyways, thanks

Jess x