> Mike's function, f(x) = (x-1)(x-2) / (x+1)(x+2), > is a quadratic divided by a quadratic. > > Jean Gaston Darboux, "Discussion de la fraction > (ax^2 + bx + c)/(a'x^2 + b'x + c')", Nouvelles > Annales de Mathematiques (2) 8 (1869), 81-86. > http://books.google.com/books?id=jRgAAAAAMAAJ&pg=PA81 >\ > Those interested in a challenge might want to consider > how you can use non-calculus concepts (quadratic formula > and max/min of parabolas topics) to investigate where > the graph of y = (ax^2 + bx + c)/(dx^2 + ex + f) has > a local maximum value and/or a local minimum value.
> We begin by rewriting the equation in implicit form > as a quadratic expression in the variable x: > > x^2y + 3xy + 2y = x^2 - 3x + 2 > > (y-1)x^2 + 3(y+1)x + 2(x-1) = 0 >
I got lost with the words "We begin by rewriting the equation..."
Which equation again? Not Mike's. Not Darboux's.
I wasn't able to find an equation in x and y only, that's being rewritten.