Question

Is anyone familiar with Continued-Fractions approximation?

Answer 1

$${x^2+3x+2 \over x^2-x+1}$$

Answer 2

Like I sooo dont follow the process although everyone seems to say that it is simple

Answer 3

continued fraction is simple, i spose this would follow its pattern

Answer 4

...if i could recall how to do a continued fraction that is. i seem to have had misremembered the simple details :)

Answer 5

\[\frac{5}{12}=\frac{1}{\cfrac{12}{5}}=\cfrac{1}{2+\cfrac25}=\cfrac{1}{2+\cfrac1{\cfrac52}}=\cfrac{1}{2+\cfrac1{2+\frac12}}\]stuff

Answer 6

This is something new, I think.

A variant on polynomial division?

Answer 7

Right but how would u clean everything up in the end. Like the answer doesnt look like an escalator in my book

Answer 8

hmm, how does it look in your book?

Answer 9

I do think its a variation of polynomial division
The answer is
$$1+{4 \over x- \frac{5}{4}} +{ \frac{21}{16} \over x + \frac{1} {4}}$$

Answer 10

I guess it's poly division as opposed to the usual integer division.

It's not that clear how u get rid of the escalator, though....

Answer 11

Oh, I see...it stops pretty quickly and then you just add up the terms.

So 1 + 1 over (blah above) and actually flipping it over so to speak...