
Re: Enrichment
Posted:
Aug 22, 2012 11:06 AM


Dave L. Renfro wrote (in part):
http://mathforum.org/kb/message.jspa?messageID=7871436
>> Mike's function, f(x) = (x1)(x2) / (x+1)(x+2), >> is a quadratic divided by a quadratic.
[snip]
>> 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 >> >> (y1)x^2 + 3(y+1)x + 2(x1) = 0
Kirby Urner wrote:
http://mathforum.org/kb/message.jspa?messageID=7872321
> 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.
I was putting Mike's equation in implicit form, after replacing f(x) by y (since we're working in the standard (x,y) coordinate plane).
y = (x1)(x2) / (x+1)(x+2)
y = (x^2  3x + 2) / (x^2 + 3x + 2)
y(x^2 + 3x + 2) = x^2  3x + 2
yx^2 + 3xy + 2y = x^2  3x + 2
yx^2 + 3xy + 2y  x^2 + 3x  2 = 0
(yx^2  x^2) + (3xy + 3x) + (2y  2) = 0
(y1)x^2 + 3(y+1)x + 2(y1) = 0
I see now that there is a typo in my last equation quoted in your post, however. I wrote "2(x1)", but it should have been "2(y1)".
Dave L. Renfro

